[1] A. Abdollahi, S. Akbari and H. R. Maimani, Non-commuting graph of a group, J. Algebra, 298 (2006) no. 2 468–492.
[2] A. Abdollahi and A. M. Hassanabadi, Noncyclic graph of a group, Comm. Algebra, 35 no. 7 (2007) 2057–2081.
[3] A. Abdollahi and A. M. Hassanabadi, Non-cyclic graph associated with a group, J. Algebra Appl., 8 (2009) 243–257.
[4] S. Abe and N. Iiyori, A generalization of prime graphs of finite groups, Hokkaido Math. J., 29 no. 2 (2000) 391–407.
[5] N. Ahanjideh, On Thompson’s conjecture for some finite simple groups, J. Algebra, 344 (2011) 205–228.
[6] N. Ahanjideh, Thompson’s conjecture for some finite simple groups with connected prime graph, Algebra Logic., 51 (2013) 2013 451–478.
[7] N. Ahanjideh, On the Thompson’s conjecture on conjugacy classes sizes, Internat. J. Algebra Comput., 23 no. 1 (2013) 37–68.
[8] N. Ahanjideh, Thompson’s conjecture for finite simple groups of Lie type Bn and Cn , J. Group Theory, 19 no. 4 (2016) 713–733.
[9] N. Ahanjideh, Thompson’s conjecture on conjugacy class sizes for the simple group PSUn (q), Internat. J. Algebra Comput., 27 no. 6 (2017) 769–792.
[10] N. Ahanjideh and M. Ahanjideh, On the validity of Thompson’s conjecture for finite simple groups, Comm. Algebra, 41 no. 11 (2013) 4116–4145.
[11] N. Ahanjideh and B. Asadian, NSE characterization of some alternating groups, J. Algebra Appl., 14 no. 2 (2015) 14 pp.
[12] M. Akbari, X. Y. Chen and A. R. Moghaddamfar, OD-characterization of some simple unitary groups, Bull.
Iranian Math. Soc., 47 no. 1 (2021) 197–215.
[13] S. H. Alavi and A. Daneshkhah, A new characterization of alternating and symmetric groups, J. Appl. Math. Comput., 17 no. 1-2 (2005) 245–258.
[14] E. Artin, The orders of the classical simple groups, Comm. Pure. Appl. Math., 8 (1955) 455–472.
[15] A. Khalili Asboei,Recognition of 2-dimensional projective linear groups by the group order and the set of numbers of its elements of each order, Groups Complex. Cryptol., 10 no. 2 (2018) 111–118.
[16] C. Bellotti, T. M. Keller and T. S. Trudgian, New bounds for numbers of primes in element orders of finite groups, Math. Nachr., 296 no. 11 (2023) 5227–5231.
[17] H. Bender, A group theoretic proof of Burnside’s pa q b -theorem, Math. Z., 126 (1972) 327–338.
[18] J. X. Bi, A characteristic property of symmetric groups (in Chinese), Acta Math. Sinica, 33 no. 1 (1990) 70–77.
[19] J. X. Bi, Characterization of alternating groups by orders of normalizers of Sylow subgroups, Algebra Colloq., 8 no. 3 (2001) 249–256.
[20] J. X. Bi and X. H. Li, A characterization of alternating groups by orders of solvable subgroups, J. Algebra Appl., 3 no. 4 (2004) 445–452.
[21] J. Brachter and P. Schweitzer, A systematic study of isomorphism invariants of finite groups via the Weisfeiler-Leman dimension, 30th annual European Symposium on Algorithms, Art, no. 27 14 pp., LIPIcs. Leibniz Int. Proc. Inform., 244, Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, 2022.
[22] R. Brandl, Finite groups all of whose elements are of prime power order, Boll. Un. Mat. Ital. A (5), 18 no. 3 (1981) 491–493.
[23] R. Brandl and W. J. Shi, Finite groups whose element orders are consecutive integers, J. Algebra, 143 no. 2 (1991) 388–400.
[24] R. Brandl and W. J. Shi, A characterization of finite simple groups with Abelian Sylow 2-subgroups, Ricerche Mat., 42 no. 1 (1993) 193–198.
[25] R. Brauer, On groups whose order contains a prime to the first power I, II., Amer. J. Math., 64 (1942) 401–440.
[26] R. Brauer and K. A. Fowler, On groups of even order, Ann. of Math. (2), 62 (1955) 565–583.
[27] T. Breuer, R. M. Guralnick, W. M. Kantor, Probabilistic generation of finite simple groups, II., J. Algebra, 320 no. 2 (2008) 443–494.
[28] Y. Bugeaud, Z. Cao and M. Mignotte, On simple K4 -groups, J. Algebra, 241 no. 2 (2001) 658–668.
[29] W. Burnside, On Groups of Order palphaqbeta, Proc. London Math. Soc. (2), 1 (1904) 388–392.
[30] A. A. Buturlakin, R. L. Shen and W. J. Shi, A characterizing property of CP -groups, Sib. Math. J., 58 no. 3 (2017) 405–407.
[31] P. J. Cameron, Graphs defined on groups, Int. J. Group Theory, 11 no. 2 (2022) 53–107.
[32] P. J. Cameron and B. Kuzma, Between the enhanced power graph and the commuting graph, J. Graph Theory, 102 no. 2 (2023) 295–303.
[33] P. J. Cameron and N. V. Maslova, Criterion of unrecognizability of a finite group by its Gruenberg-Kegel graph, J. Algebra, 607 part A (2022) 186–213.
[34] A. R. Camina and R. D. Camina, The influence of conjugacy class sizes on the structure of finite groups: a survey, Asian-Eur. J. Math., 4 no. 4 (2011) 559–588.
[35] H. P. Cao, G. Y. Chen, M. A. Grechkoseeva et al., Recognition of the finite simple groups F4 (2m ) by spectrum, Siberian Math. J., 45 no. 6 (2004) 1031–1035.
[36] H. P. Cao and W. J. Shi, Pure quantitative characterization of finite projective special unitary groups, Sci. China Ser. A, 45 no. 6 (2002) 761–772.
[37] G. Y. Chen, On Thompson’s conjecture (in Chinese), In: Proceedings of the China Association for Science and Technology First Academic Annual Meeting of Youths, Beijing: China Sci and Tech Press, 1992 1-6.
[38] G. Y. Chen, A new characterization of sporadic simple groups, Algebra Colloq., 3 no. 1 (1996) 49–58.
[39] G. Y. Chen, On Thompson’s conjecture, J. Algebra, 185 no. 1 (1996) 184–193.
[40] G. Y. Chen, Further reflections on Thompson’s conjecture, J. Algebra, 218 no. 1 (1999) 276–285.
[41] G. Y. Chen, Characterization of 3D4 (q), Southeast Asian Bull. Math., 25 no. 3 (2001) 389–401.
[42] G. Y. Chen and W. J. Shi, Finite groups with 30 elements of maximal order, Appl. Categ. Structures, 16 no. 1-2 (2008) 239–247.
[43] Z. M. Chen, On orders of finite simple groups, (Chinese), Acta Math. Sinica, 30 no. 5 (1987) 605–613.
[44] K. N. Cheng , M. Deaconescu, M. L. Lang and W. J. Shi, Corrigendum and addendum to: “Classification of finite groups with all elements of prime order”, Proc. Amer. Math. Soc., 117 no. 4 (1993) 1205–1207.
[45] N. Chigira and W. J. Shi, More on the set of element orders in finite groups, Northeast. Math. J., 12 no. 3 (1996) 257–260.
[46] J. H. Conway, R. T. Curtis, S. P. Norton et al., ATLAS of finite groups. Maximal subgroups and ordinary characters for simple groups, Oxford: Oxford University Press, 1985.
[47] M. Deaconescu, Classification of finite groups with all elements of prime order, Proc. Amer. Math. Soc., 106 no. 3 (1989) 625–629.
[48] K. Denecke, X. H. Li and J. X. Bi, A characterization of finite simple groups by the orders of solvable subgroups, Sci. China Ser. A, 50 no. 5 (2007) 715–726.
[49] H. W. Deng, The number of elements of type pq in the set of element orders and group structure, Group theory (Beijing, 1996), Springer, Singapore, 1998 80–87.
[50] H. W. Deng and W. J. Shi, A simplicity criterion for finite groups, J. Algebra, 191 no. 1 (1997) 371–381.
[51] H. W. Deng and W. J. Shi, The characterization of Ree groups 2 F4 (q) by their element orders, J. Algebra, 217 no. 1 (1999) 180–187.
[52] C. Y. Dong and G. Mason, Moonshine, the Monster, and Related Topics, American Mathematical Society, Mathematics,1994 p. 368.
[53] L. E. Dickson, A new extension of Dirichlet¡¯s theorem on prime numbers, Messenger. Math., 33 (1904) 155–161.
[54] A. Dress, A characterisation of solvable groups, Math. Z., 110 (1969) 213–217.
[55] X. L. Du and Y. Y. Jiang, Finite groups with exactly 4p maximal order elements, (in Chinese), Chinese Ann. Math. Ser. A, 25 no. 5 (2004) 607–612.
[56] W. Feit and G. M. Seitz, On finite rational groups and related topics, Illinois J. Math., 33 no. 1 (1989) 103–131.
[57] W. Feit and J. G. Thompson, Solvability of groups of odd order, Pacific J. Math., 13 (1963) 775–1029.
[58] Y. Q. Feng, Finite groups whose abelian subgroup orders are consecutive integers, J. Math. Res. Exposition, 18 no. 4 (1998) 503–506.
[59] P. Fitzpatrick, Order conjugacy in finite groups, Proc. Roy. Irish Acad. Sect. A, 85 no. 1 (1985) 53–58.
[60] Y. W. Gao and H. P. Cao, On a new characterization of the automorphism groups of sporadic simple groups, (in Chinese), J. Southwest China Normal Univ. (Natur. Sci. Ed.), 38 no. 2 (2013) 1–5.
[61] D. M. Goldschmidt, A group theoretic proof of the pa q b theorem for odd primes, Math. Z., 113 (1970) 373–375.
[62] D. Gorenstein, R. Lyons and R. Solomon, The classification of the finite simple groups, The generic case, completed, Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, Number 8 Part III (2018) Chapters 12–17.
[63] I. B. Gorshkov, Thompson’s conjecture for simple groups with a connected prime graph, Algebra Logic, 51 no. 2 (2012) 111–127.
[64] I. B. Gorshkov, Recognizability of alternating groups by the spectrum, Algebra Logic, 52 no. 1 (2013) 41–45
[65] I. B. Gorshkov, Towards Thompson’s conjecture for alternating and symmetric groups, J. Group Theory, 19 no. 2 (2016) 331–336.
[66] I. B. Gorshkov, Thompson’s conjecture for alternating and symmetric groups of degree greater than 1361, Proc. Steklov Inst. Math., 293 (2016) 58–65.
[67] I. B. Gorshkov, On Thompson’s conjecture for alternating groups of large degree, J. Group Theory, 20 no. 4 (2017) 719–728.
[68] I. B. Gorshkov, Thompson’s conjecture for alternating groups, Comm. Algebra, 47 no. 1 (2019) 30–36.
[69] I. B. Gorshkov, On Thompson’s conjecture for finite simple groups, Comm. Algebra, 47 no. 12 (2019) 5192–5206.
[70] I. B. Gorshkov, I. B. Kaygorodov, A. V. Kukharev and A. A. Shlepkin, On Thompson’s conjecture for finite simple exceptional groups of Lie type, J. Math. Sci. (N.Y.), 247 no. 4 (2020) 565–570.
[71] I. B. Gorshkov and A. V. Kukharev, Finite groups with prime graphs of diameter 5, Commun. Math., 28 no. 3 (2020) 307–312.
[72] I. B. Gorshkov and N. V. Maslova, The group J4 × J4 is recognizable by spectrum, J. Algebra Appl., 20 no. 4 (2021) 14 pp.
[73] M. A. Grechkoseeva, On the difference between spectra of the simple groups Bn (q) and Cn (q), Siberian Math. J., 48 no. 1 (2007) 73–75.
[74] M. A. Grechkoseeva, Recognition by spectrum for finite linear groups over fields of characteristic 2, Algebra Logic, 47 no. 4 (2008) 229–241.
[75] M. A. Grechkoseeva, V. D. Mazurov, W. J. Shi et al. Finite groups isospectral to simple groups, Commun. Math. Stat., 11 no. 2 (2023) 169–194.
[76] M. A. Grechkoseeva and A. V. Vasil’ev, On the structure of finite groups isospectral to finite simple groups, J. Group Theory, 18 no. 5 (2015) 741–759.
[77] J. A. Grochow and M. Levet, On the parallel complexity of group isomorphism via Weisfeiler-Leman, Fundamentals of computation theory, Lecture Notes in Comput. Sci., Springer, Cham, 2023 234–247.
[78] W. Guo, A. S. Kondrat’ev and N. V. Maslova, Recognition of the group E6 (2) by Gruenberg-Kegel graph, Tr. Inst. Mat. Mekh., 27 no. 4 (2021) 263–268.
[79] N. D. Gupta and V. D. Mazurov, On groups with small orders of elements, Bull. Austral. Math. Soc., 60 no. 2 (1999) 197–205.
[80] M. Hagie, The diameter of the solvable graph of a finite group, Hokkaido Math. J., 29 no. 3 (2000) 553–561.
[81] M. Jr. Hall, The theory of groups, Reprinting of the 1968 edition, Chelsea Publishing Co., New York, 1976.
[82] J. H. He and W. Pu, On the number n which makes any group with order prime to n solvable, (in Chinese), J. Southwest China Normal Univ. (Natur. Sci. Ed.), 24 (1999) 612–614.
[83] L. G. He and G. Y. Chen, A new characterization of simple K3 -groups, Comm. Algebra, 40 no. 10 (2012) 3903–3911.
[84] L. G. He and G. Y. Chen, A new characterization of simple K4 -groups with type L2 (p), Adv. Math. (China), 43 no. 5 (2014) 667–670.
[85] L. G. He, G. Y. Chen and H. J. Xu, A new characterization of sporadic simple groups, Ital. J. Pure Appl. Math., No. 30 (2013) 373–392.
[86] L. G. He, G. Y. Chen and Y. X. Yan, Finite groups with 10pm elements of maximal order are solvable, (in Chinese), J. Southwest Univ. (Natur. Sci. Ed.), 29 2007 1–4.
[87] L. G. He and H. J. Xu, A characterization of automorphism groups of K3 -groups, (Chinese) Adv. Math. (China), 44 no. 3 (2015) 363–368.
[88] H. Heineken, On groups all of whose elements have prime power order, Math. Proc. R. Ir. Acad., 106A no. 2 (2006) 191–198.
[89] M. Herzog, On finite simple groups of order divisible by three primes only, J. Algebra, 10 (1968) 383–388.
[90] G. Higman, Finite groups in which every element has prime power order, J. London Math. Soc., 32 (1957) 335–342.
[91] N. N. Hung and Y. Yang, On the prime divisors of element orders, Math. Nachr., 294 no. 10 (2021) 1905–1911.
[92] B. Huppert and W. Lempken, Simple groups of order divisible by at most four primes, Proc. F. Scorina Gomel State Univ., 16 no. 3 (2000) 64-75.
[93] N. Iiyori and H. Yamaki, Prime graph components of the simple groups of Lie type over the field of even characteristic, J. Algebra, 155 no. 2 (1993) 335–343.
[94] A. Iranmanesh and B. Khosravi, A characterization of F4 (q) where q is an odd prime power, Groups St. Andrews 2001 in Oxford, Vol. I, London Math. Soc. Lecture Note Ser., 304, Cambridge Univ. Press, Cambridge, 2003 277–283.
[95] E. Jabara, D. V. Lytkina and V. D. Mazurov, Some groups of exponent 72, J. Group Theory, 17 no. 6 (2014) 947–955.
[96] A. Jafarzadeh and A. Iranmanesh, On simple Kn -groups for n = 5, 6, Groups St. Andrews 2005, Vol. 2, London Math. Soc. Lecture Note Ser., 340, Cambridge Univ. Press, Cambridge, 2007 517–526.
[97] Q. H. Jiang and C. G. Shao, Finite groups with 24 elements of maximal order, Front. Math. China, 5 no. 4 (2010) 665–678.
[98] Y. Y. Jiang, Finite solvable groups with the number of largest element orders less than 20, (in Chinese), J. Southwest China Normal Univ. (Natur. Sci. Ed.), 23 no. 4 (1998) 379–384.
[99] Y. Y. Jiang, Finite groups having 2p2 elements of maximal order are solvable, (Chinese), Chinese Ann. Math. Ser. A, 21 no. 1 (2000) 61–64.
[100] Y. Y. Jiang, A theorem of finite groups with 18p elements having maximal order, Algebra Colloq., 15 no. 2 (2008) 317–329.
[101] Y. Y. Jiang and G. H. Qian, Finite groups having 6p elements of maximal order, (Chinese), Chinese Ann. Math. Ser. A, 27 no. 3 (2006) 325–330.
[102] W. M. Kantor and Á. Seress, Large element orders and the characteristic of Lie-type simple groups, J. Algebra, 322 no. 3 (2009) 802–832.
[103] A. V. Kelarev and S. J. Quinn, A combinatorial property and power graphs of groups Contributions to general algebra, 12 (Vienna, 1999), Heyn, Klagenfurt, 2000 229–235.
[104] T. M. Keller, Solvable groups with a small number of prime divisors in the element orders, J. Algebra, 170 no. 2 (1994) 625–648.
[105] T. M. Keller, Solvable groups with at most four prime divisors in the element orders, J. Algebra, 175 no. 1 (1995) 1–23.
[106] T. M. Keller, A linear bound for ρ(n), J. Algebra, 178 no. 2 (1995) 643–652.
[107] T. M. Keller and A. Moretó, Character degrees, conjugacy class sizes, and element orders: three primes, Arch. Math. (Basel), 117 no. 3 (2021) 241–251.
[108] B. Khosravi, A characterization of E6 (Q), Algebras Groups Geom., 19 no. 2 (2002) 225–243.
[109] B. Khosravi and B. Khosravi, A characterization of 2 E6 (q), Kumamoto J. Math., 16 (2003) 1–11.
[110] A. P. Khramova, N. V. Maslova, V. V. Panshin and A. M. Staroletov, Characterization of groups E6 (3) and 2 E6 (3) by Gruenberg-Kegel graph, Sib. Èlektron Mat. Izv., 18 no. 2 (2021) 1651–1656.
[111] E. I. Khukhro and V. D. Mazurov, Unsolved problems in group theory. The Kourovka notebook, No. 20, arXiv:1401.0300v26, 2022.
[112] W. Kimmerle, F. Luca and A. G. Raggi-Cárdenas, Irreducible components and isomorphisms of the Burnside ring, J. Group Theory, 11 no. 6 (2008) 831–844.
[113] A. S. Kondrat’ev, Prime graph components of finite simple groups, Math. USSR-Sb., 67 no. 1 (1990) 235–247.
[114] A. S. Kondrat’ev and V. D. Mazurov, Recognition of alternating groups of prime degree from their element orders, Siberian Math. J., 41 no. 2 (2000) 294–302.
[115] A. S. Kondrat’ev, Recognizability by spectrum of groups E8 (q), Tr. Inst. Mat. Mekh. UrO RAN, 16 no. 3 (2010) 146–149.
[116] A. S. Kondrat’ev, Finite almost simple 5-primary groups and their Gruenberg-Kegel graphs, Sib. Èlektron. Mat. Izv., 11 (2014) 634–674.
[117] A. S. Kondrat’ev and V. D. Mazurov, Recognition of alternating groups of prime degree from the orders of their elements, Sibirsk. Mat. Zh., 41 no. 2(2000) 359–369.
[118] A. Kumar, L. Selvaganesh, P. J. Cameron and T. Tamizh Chelvam, Recent developments on the power graph of finite groups—a survey, AKCE Int. J. Graphs Comb., 18 no. 2 (2021) 65–94.
[119] M. L. Lewis, Groups having all elements off a normal subgroup with prime power order, Vietnam J. Math., 51 no. 3 (2023) 577–587.
[120] J. B. Li, W. J. Shi and D. P. Yu, A characterization of some P GL(2, q) by maximum element orders, Bull. Korean Math. Soc., 52 no. 6 (2015) 2025–2034.
[121] J. H. Li, Finite groups with element orders of odd consecutive integers, (in Chinese), J. Southwest China Normal Univ. (Natur. Sci. Ed.), 19 (1994) 109–115.
[122] T. Li, A. R. Moghaddamfar, A. V. Vasil’ev and Zh. Wang, On recognition of the direct squares of the simple groups with abelian Sylow 2-subgroups, Ric. Mat., 74 (2025), no. 1, 61--78.
[123] X. H. Li, A characterization of the finite simple groups, J. Algebra, 245 no. 2 (2001) 620–649.
[124] Y. Li and W. J. Shi, A note on Thompson problem, Ric. Mat., 74 (2025), no. 1, 559--563.
[125] M. W. Liebeck and A. Shalev, Simple groups, probabilistic methods, and a conjecture of Kantor and Lubotzky, J. Algebra, 184 no. 1 (1996) 31–57.
[126] S. T. Liu and Y. Huang, On Thompson’s conjecture for alternating group A26 , Ital. J. Pure Appl. Math., No. 32 (2014) 525–532.
[127] M. S. Lucido, The diameter of the prime graph of a finite group, J. Group Theory, 2 no. 2 (1999) 157–172.
[128] M. S. Lucido, Groups in which the prime graph is a tree, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8), 5 no. 1 (2002) 131–148.
[129] D. V. Lytkina and A. A. Kuznetsov, Recognizability by spectrum of the group L2 (7) in the class of all groups, Sib. Èlektron. Mat. Izv., 4 (2007) 136–140.
[130] D. V. Lytkina and V. D. Mazurov, Groups containing a strongly embedded subgroup, Algebra Logic, 48 no. 2 (2009) 108–114.
[131] D. V. Lytkina and V. D. Mazurov, Periodic groups generated by a pair of virtually quadratic automorphisms of an abelian group, Sib. Math. J., 51 no. 3 (2010) 475–478
[132] D. V. Lytkina and V. D. Mazurov, {2, 3}-groups with no elements of order 6, Algebra Logic, 53 (2015) 463-470.
[133] D. V. Lytkina and V. D. Mazurov, On groups of period 12, Sib. Math. J., 56 no. 3 (2015) 471–475.
[134] D. V. Lytkina, V. D. Mazurov and A. S. Mamontov, On local finiteness of some groups of period 12, Sib. Math. J., 53 no. 6 (2012) 1105–1109.
[135] D. V. Lytkina, V. D. Mazurov, A. S. Mamontov and È. Yabara, Groups whose element orders do not exceed 6, Algebra Logic, 53 no. 5 (2014) 365–376.
[136] A. S. Mamontov and E. Jabara, Recognizing A7 by its set of element orders, Sib. Math. J., 62 no. 1 (2021) 93–104.
[137] N. V. Maslova, V. V. Panshin and A. M. Staroletov, On characterization by Gruenberg-Kegel graph of finite simple exceptional groups of Lie type, Eur. J. Math., 9 no. 3 (2023) 17 pp.
[138] H. Matsuyama, Solvability of groups of order 2a pb , Osaka Math. J., 10 (1973) 375–378.
[139] V. D. Mazurov, The set of orders of elements in a finite group, Algebra Logic, 33 (1994) 49–55.
[140] V. D. Mazurov, Characterizations of finite groups by sets of orders of their elements, Algebra Logic, 36 no. 1 (1997) 23–32.
[141] V. D. Mazurov, A characterization of finite nonsimple groups by the set of orders of their elements, Algebra Logic, 36 (1997)182–192.
[142] V. D. Mazurov, Recognition of finite groups by a set of orders of their elements, Algebra Logic, 37 no. 6 (1998) 371–379.
[143] V. D. Mazurov, Infinite groups with Abelian centralizers of involutions, Algebra Logic, 39 no. 1 (2000) 42–49.
[144] V. D. Mazurov, Groups of exponent 60 with prescribed orders of elements, Algebra Logic, 39 no. 3 (2000) 189–198.
[145] V. D. Mazurov Groups containing a self-centralizing subgroup of order 3, Algebra Logic, 42 (2003) 29–36.
[146] V. D. Mazurov, Characterizations of groups by arithmetic properties, Proceedings of the International Conference on Algebra, Algebra Colloq., 11 no. 1 (2004) 129–140.
[147] V. D. Mazurov, Groups of exponent 24, Algebra Logic, 49 no. 6 (2011) 515–525.
[148] V. D. Mazurov and A. S. Mamontov, On periodic groups with small orders of elements, Sib. Math. J., 50 no. 2 (2009) 316–321.
[149] V. D. Mazurov and A. S. Mamontov, Involutions in groups of exponent 12, Algebra Logic, 52 no. 1 (2013) 67–71.
[150] V. D. Mazurov, A. Y. Ol’shanskii and A. I. Sozutov, Infinite groups of finite period, Algebra Logic, 54 no. 2 (2015) 161–166.
[151] V. D. Mazurov and W. J. Shi, A note to the characterization of sporadic simple groups. Algebra Colloq., 5 no. 3 (1998) 285–288.
[152] V. D. Mazurov and W. J. Shi, Groups whose elements have given orders, Groups St. Andrews 1997 in Bath, II, London Math. Soc. Lecture Note Ser., 261, Cambridge Univ. Press, Cambridge, 1999 532–537.
[153] V. D. Mazurov and W. J. Shi, A criterion of unrecognizability by spectrum for finite groups, Algebra Logic, 51 (2012) 160–162.
[154] A. R. Moghaddamfar, About noncommuting graphs, Siberian Math. J., 47 no. 5 (2006) 911–914.
[155] A. R. Moghaddamfar and M. R. Darafsheh, A family of finite simple groups which are 2-recognizable by their elements order, Comm. Algebra, 32 no. 11 (2004) 4507–4513.
[156] A. R. Moghaddamfar, S. Rahbariyan and W. J. Shi, Certain properties of the power graph associated with a finite group, J. Algebra Appl., 13 no. 7 (2014) 18 pp.
[157] A. R. Moghaddamfar, W. J. Shi, W. Zhou and A. R. Zokayi, On the noncommuting graph associated with a finite group, Siberian Math. J., 46 no. 2 (2005) 325–332.
[158] A. R. Moghaddamfar and A. R. Zokayi, Recognizing finite groups through order and degree pattern, Algebra Colloq., 15 no. 3 (2008) 449–456.
[159] A. R. Moghaddamfar and A. R. Zokayi, OD-characterization of alternating and symmetric groups of degrees 16 and 22, Front. Math. China, 4 no. 4 (2009) 669–680.
[160] A. R. Moghaddamfar, A. R. Zokayi and M. R. Darafsheh, A characterization of finite simple groups by the degrees of vertices of their prime graphs, Algebra Colloq., 12 no. 3 (2005) 431–442.
[161] A. Moretó, On the number of different prime divisors of element orders, Proc. Amer. Math. Soc., 134 no. 3 (2006) 617–619.
[162] G. Navarro, The set of conjugacy class sizes of a finite group does not determine its solvability. J. Algebra, 411 (2014) 47–49.
[163] G. Navarro, Character Theory and the McKay Conjecture, Cambridge Studies in Advanced Mathematics, 175, Cambridge University Press, Cambridge, 2018.
[164] B. H. Neumann, A problem of Paul Erdös on groups, J. Austral. Math. Soc. Ser. A, 21 no. 4 (1976) 467–472.
[165] C. E. Praeger and W. J. Shi, A characterization of some alternating and symmetric groups, Comm. Algebra, 22 no. 5 (1994) 1507–1530.
[166] G. H. Qian, Finite groups with many elements of prime order, (Chinese) J. Math. (Wuhan), 25 no. 1 (2005) 115–118.
[167] G. H. Qian, Finite groups with consecutive nonlinear character degrees, J. Algebra, 285 (2005) no. 1 372–382.
[168] G. H. Qian, Element orders and character codegrees, Bull. Lond. Math. Soc., 53 no. 3 (2021) 820–824.
[169] G. H. Qian, Finite solvable groups whose prime graphs have diameter 3, Acta. Math. Sin. (Engl Ser.), (2023), in press.
[170] G. H. Qian and W. J. Shi, A characteristic property of A5 and its elementary proof, (in Chinese), J. Southwest Univ. (Natur. Sci. Ed.), 29 (2007) 1–4.
[171] G. H. Qian, Y. Wang and H. Q. Wei, Co-degrees of irreducible characters in finite groups, J. Algebra, 312 no. 2 (2007) 946–955.
[172] R. L. Shen, C. G. Shao, Q. H. Jiang et al, A new characterization of A5 , Monatsh. Math., 160 no. 3 (2010) 337–341.
[173] R. L. Shen and W. J. Shi, On Thompson problem, (in Chinese), Sci. Sin. Math., 40 2010 533–537.
[174] R. L. Shen, F. Tang and W. J. Shi, Corrigendum to On Thompson Problem, Sci. Sin. Math., 40 no. 6 (2010) (in Chinese), Sci. Sin. Math., 41 (2011) 933–938.
[175] Z. Shen, B. Zhang, J. Zhang et al. new characterization of sporadic simple group M22 via its vanishing elements, Front. Math., 19 no. 3 (2024), 551–558.
[176] W. J. Shi, A new characterization of some projective special linear groups and the finite groups in which every element has prime order or order 2p, J. Southwest-China Teachers University (N.S.), 8 (1983) 23–28.
[177] W. J. Shi, A characteristic property of PSL2 (7), J. Austral. Math. Soc. Ser. A, 36 no. 3 (1984) 354–356.
[178] W. J. Shi, A characterization of some PSL2 (q), (in Chinese), J. Southwest-China Teachers. Univ. (N. S.), (1985) 10 25-32.
[179] W. J. Shi, A characterization of some projective special linear groups, J. Math. (Wuhan), 5 no. 2 (1985) 191–200.
[180] W. J. Shi, A characteristic property of A5 , (in Chinese), J. Southwest China Normal Univ. (Natur. Sci. Ed.), 11 (1986) 11–14.
[181] W. J. Shi, A characterization of J1 and PSL2 (2n ), (Chinese) Adv. in Math. (Beijing), 16 no. 4 (1987) 397–401.
[182] W. J. Shi, A new characterization of the sporadic simple groups, Group theory (Singapore, 1987), de Gruyter, Berlin, 1989 531–540.
[183] W. J. Shi, Using orders to characterize simple groups and related topics, (Chinese), Adv. in Math. (China), 20 no. 2 (1991) 135–141.
[184] W. J. Shi, On simple K4 groups, (in Chinese), Chin. Sci. Bull., 36 (1991) 1281–1283.
[185] W. J. Shi, On a problem of E. Artin, (Chinese), Acta Math. Sinica, 35 no. 2 (1992) 262–265.
[186] W. J. Shi, A characterization of Suzuki’s simple groups, Proc. Amer. Math. Soc., 114 no. 3 (1992) 589–591.
[187] W. J. Shi, The characterization of the sporadic simple groups by their element orders, Algebra Colloq., 1 no. 2 (1994) 159–166.
[188] W. J. Shi, Finite groups whose proper subgroup orders are consecutive integers, J. Math. Res. Exposition, 14 no. 2 (1994) 165–166.
[189] W. J. Shi, Pure quantitative characterization of finite simple groups. I., Progr. Natur. Sci. (English Ed.), 4 no. 3 (1994) 316–326.
[190] W. J. Shi, Two unsolved problems in group theory, (in Chinese), J. Southwest China Normal Univ. (Natur. Sci. Ed.), (1996), 21 6–10.
[191] W. J. Shi, Finite groups defined by the sets of their element orders, Xinan Shifan Daxue Xuebao Ziran Kexue Ban, 22 no. 5 (1997) 481–486.
[192] W. J. Shi, Groups whose elements have given orders, Chinese Sci. Bull., 42 no. 21 (1997) 1761–1764.
[193] W. J. Shi, Pure quantitative characterization of finite simple groups, Front. Math. China, 2 no. 1 (2007) 123–125.
[194] W. J. Shi, On the order and the element orders of finite groups: results and problems, Ischia group theory, 2010, World Sci. Publ., Hackensack, NJ, 2012 313–333.
[195] W. J. Shi, A sufficient condition for solvability of finite groups, (in Chinese), J. Southwest Univ. (Natur. Sci. Ed.), 37 (2017) 1–4.
[196] W. J. Shi, On the widths of finite groups, Southeast Asian Bull. Math., 45 no. 6 (2021) 945–951.
[197] W. J. Shi and J. X. Bi, A characteristic property for each finite projective special linear group, Groups—Canberra 1989, Lecture Notes in Math., 1456, Springer, Berlin, 1990, 171–180.
[198] W. J. Shi and J. X. Bi, A characterization of Suzuki-Ree groups, Sci. China Ser. A, 34 no. 1 (1991) 14–19.
[199] W. J. Shi and J. X. Bi, A new characterization of the alternating groups, Southeast Asian Bull. Math., 16 (1992) no. 1 81–90.
[200] W. J. Shi and C. Y. Tang, A characterization of some orthogonal groups, Prog. Nat. Sci., 1997, 7 155–162.
[201] W. J. Shi and W. Z. Yang, A new characterization of A5 and finite groups in which every element order is a prime power order, (in Chinese), J. Southwest China Normal Univ. (Natur. Sci. Ed.), 9 (1984) 36–40.
[202] W. J. Shi and W. Z. Yang, On finite groups with elements of prime power orders, (in Chinese), J. Yunnan Education Coll., 1 (1986) 2–10, arXiv:2003.09445.
[203] R. Solomon, A brief history of the classification of the finite simple groups, Bull. Amer. Math. Soc. (N.S.), 38 no. 3 (2001) 315–352.
[204] A. M. Staroletov, Groups isospectral to the alternating group of degree 10, Sib. Math. J., 51 no. 3 (2010) 507–514.
[205] M. Suzuki, Finite groups with nilpotent centralizers, Trans. Amer. Math. Soc., 99 (1961) 425–470.
[206] S. B. Tan, H. M. Ai and Y. X. Yan, Finite groups with 6p2 q elements of maximal order, (in Chinese), J. Southwest China Normal Univ. (Natur. Sci. Ed.), 46 (2021) 1–3.
[207] J. G. Thompson, Nonsolvable finite groups all of whose local subgroups are solvable, Bull. Amer. Math. Soc., 74 (1968) 383–437.
[208] R. W. van der Waall and A. Bensaid, On finite groups whose elements of equal order are conjugate, Simon Stevin, 65 no. 3-4 (1991) 361–374.
[209] A. V. Vasil’ev, On the recognition of all finite nonabelian simple groups with orders having prime divisors at most 13, Siberian Math. J., 46 (2005) 246–253.
[210] A. V. Vasil’ev, On Thompson’s conjecture, Sib. Èlektron. Mat. Izv., 6 (2009) 457–464.
[211] A. V. Vasil’ev, M. A. Grechkoseeva and V. D. Mazurov, On finite groups isospectral to simple symplectic and orthogonal groups, Sib. Math. J., 50 no. 6 (2009) 965–981.
[212] A. V. Vasil’ev, M. A. Grechkoseeva and V. D. Mazurov, Characterization of finite simple groups by spectrum and order, Algebra Logic, 48 no. 6 (2009) 385–409.
[213] A. V. Vasil’ev and A. M. Staroletov, Recognizability of the groups G2 (q) by the spectrum, Algebra Logic, 52 no. 1 (2013) 1–14.
[214] A. V. Vasil’ev and E. P. Vdovin, An adjacency criterion in the prime graph of a finite simple group, Algebra Logic, 44 no. 6 (2005) 381–406.
[215] A. V. Vasil’ev and E. P. Vdovin, Cocliques of maximal size in the prime graph of a finite simple group, Algebra Logic, 50 no. 4 (2011) 291–322.
[216] L. L. Wang and W. J. Shi, A new characterization of A10 by its noncommuting graph, Comm. Algebra, 36 no. 2 (2008) 523–528.
[217] X. F. Wang, Classification theorem of K4 simple groups, (in Chinese), Chin. Sci. Bull., 35 (1990) 1117–1118.
[218] Zh. Wang, A. V. Vasil’ev, M. A. Grechkoseeva and A. Kh. Zhurtov, A criterion for nonsolvability of a finite group and recognition of direct squares of simple groups, Algebra Logic, 61 no. 4 (2022) 288–300.
[219] J. S. Williams, Prime graph components of finite groups, J. Algebra, 69 no. 2 (1981) 487–513.
[220] M. C. Xu, Finite groups with element orders of consecutive integers except some primes (in Chinese), J. Southwest. China Normal Univ. (Natur Sci. Ed.), 19 (1994) 116–122.
[221] M. C. Xu, On finite groups with the same order type of σ-Sylow tower groups, (in Chinese), J. Hainan Univ. (Natur. Sci.), 14 (1996) 103–105.
[222] M. C. Xu, Thompson’s conjecture for alternating group of degree 22, Front. Math. China, 8 no. 5 (2013) 1227–1236.
[223] M. C. Xu and W. J. Shi, Pure quantitative characterization of finite simple groups 2 Dn (q) and Dl (q) (lodd), Algebra Colloq., 10 no. 3 (2003) 427–443.
[224] M. C. Xu and W. J. Shi, Thompson’s conjecture for Lie type groups E7 (q), Sci. China Math., 57 no. 3 (2014) 499–514.
[225] C. Yang, Finite groups with various numbers of elements of maximum order, (Chinese), Chinese Ann. Math. Ser. A, 14 no. 5 (1993) 561–567.
[226] N. Y. Yang, D. V. Lytkina, V. D. Mazurov and A. Kh. Zhurtov, Infinite Frobenius groups generated by elements of order 3, Algebra Colloq., 27 no. 4 (2020) 741–748.
[227] W. Z. Yang and Z. R. Zhang, Locally soluble infinite groups in which every element has prime power order, Southeast Asian Bull. Math., 26 no. 5 (2003) 857–864.
[228] Y. Yang, On analogues of Huppert’s conjecture, Bull. Aust. Math. Soc., 104 no. 2 (2021) 272–277.
[229] T. Yoshida, On the Burnside rings of finite groups and finite categories, In: Commutative algebra and combinatorics, Adv. Stud. Pure Math., 11, North-Holland, Amsterdam, 1987 337–353.
[230] D. P. Yu, J. B. Li, G. Y. Chen et al. A new characterization of simple K5 -groups of type L3 (p), Bull. Iranian Math. Soc., 45 no. 3 (2019) 771–781.
[231] A. V. Zavarnitsine, Recognition of alternating groups of degrees r + 1 and r + 2 for prime r and of a group of degree 16 by the set of their element orders, Algebra and Logic, 39 no. 6 (2000) 370–377.
[232] A. V. Zavarnitsine, Recognition of the simple groups L3 (q) by element orders, J. Group Theory, 7 no. 1 (2004) 81–97.
[233] J. P. Zhang, On Syskin problem of finite groups, Sci. Sinica, 2 (1988) 189–193.
[234] J. P. Zhang, Arithmetical conditions on element orders and group structure, Proc. Amer. Math. Soc., 123 no. 1 (1995) 39–44.
[235] J. S. Zhang, On type of zeros of characters of finite groups, (in Chinese), Ph. D. Thesis, Suzhou: Soochow University, (2009).
[236] L. C. Zhang and W. J. Shi, OD-characterization of all simple groups whose orders are less than 108 , Front. Math. China, 3 no. 3 (2008) 461–474.
[237] L. C. Zhang and W. J. Shi, OD-characterization of simplex K4 -groups, Algebra Colloq. 16 no. 2 (2009) 275–282.
[238] L. C. Zhang, W. J. Shi and X. F. Liu, A characterization of L4 (4) by its noncommuting graph, (in Chinese), Chinese Ann. Math. Ser. A, 30 no. 4 (2009) 517–524.
[239] Q. H. Zhang and L. J. An, The Structure of Finite p-Groups I, (in Chinese), Beijing: Science Press, 2017.
[240] Q. H. Zhang and L. J. An, The Structure of Finite p-Groups II, (in Chinese), Beijing: Science Press, 2017.
[241] SH. Zhang and W. J. Shi, On the number of simple K4 groups, Bull. Iranian Math. Soc., 46 no. 6 (2020) 1669–1674.
[242] A. Kh. Zhurtov, D. V. Lytkina and V. D. Mazurov, On primary cosets in groups, Algebra Logic, 59 no. 3 (2020) 216–221.
[243] A. Kh. Zhurtov, D. V. Lytkina, V. D. Mazurov and A. I. Sozutov, On periodic groups freely acting on abelian groupss, Proc. Steklov Inst. Math., 285 suppl. 1 (2014) 209–215.
[244] A. Kh. Zhurtov and V. D. Mazurov, On the recognition of the finite simple groups L2 (2m ) in the class of all groups, Siberian Math. J., 40 no. 1 (1999) 62–64.
[245] A. Kh. Zhurtov and V. D. Mazurov, Frobenius groups generated by quadratic elements, Algebra Logic, 42 no. 3 (2003) 153–164.
[246] A. V. Vasil’ev, On connection between the structure of a finite group and the properties of its prime graph, Siberian Math. J., 46 no. 3 (2005) 396–404.
[247] P. Piwek, Solvable and non-solvable finite groups of the same order type, (2024) arXiv: 2403.02197v2.
[248] A. A. Buturiakin, Isospectral finite simple groups, Sib. Elektron. Mat. Izv., 7 (2010) 111–114.
[249] P. Müller, A note about solvable and non-solvable finite groups of the same order type, (2024) arXiv:2408.07732v1.
