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On pairs of antagonistic subgroups and theirs influence on the structure of groups | ||
International Journal of Group Theory | ||
مقاله 20، دوره 12، شماره 2، شهریور 2023، صفحه 81-98 اصل مقاله (433.28 K) | ||
نوع مقاله: Ischia Group Theory 2020/2021 | ||
شناسه دیجیتال (DOI): 10.22108/ijgt.2022.131896.1768 | ||
نویسندگان | ||
Leonid A. Kurdachenko1؛ Patrizia Longobardi2؛ Mercede Maj* 2؛ Javier Otal3 | ||
1Department of Algebra and Geometry School of Mathematics and Mechanics, University of Dnipro, Gagarin prospect 72, Dnipro 10, 49010 Ukraine | ||
2Dipartimento di Matematica, Università di Salerno, via Giovanni Paolo II, 132, 84084 Fisciano (Salerno), Italy | ||
3Universidad de Zaragoza, Edificio de matemáticas, C/Pedro Cerbuna 12, 50009 Zaragoza, España | ||
چکیده | ||
In this survey we collect some results on the influence on the structure of a group of some families of its subgroups satisfying conditions related to normality. In particular we focus on groups whose subgroups have two antagonistic properties. | ||
کلیدواژهها | ||
normal؛ subnormal؛ ascendant؛ descendant؛ selfnormalizing؛ abnormal؛ conormal؛ contranormal؛ pronormal subgroups | ||
مراجع | ||
[1] I. N. Abramovskii, Locally generalized Hamiltonian groups, Sibirsk. Mat. Ž, 7 (1966), 481-485.
[2] A. Ballester-Bolinches, R. Esteban-Romero, On finite T -groups, J. Aust. Math. Soc., 75 (2) (2003), 181-191.
[3] M. S. Ba, Z. I. Borevich, Arrangements of intermediate subgroups, Rings and Linear Groups, Kuban. Gos. Univ., Krasnodar, (1988), 14-41. [4] E. Best, O. Taussky, A class of groups, Proc. Roy. Irish. Acad. Sect. A., 47 (1942), 55-62.
[5] M. Bianchi, A. Gillio Berta Mauri, M. Herzog, L. Verardi, On finite solvable groups in which normality is a transitive relation, J. Group Theory, 3 (2000), 147-156. [6] R. W. Carter, Nilpotent self-normalizing subgroups of soluble groups, Math. Z., 75 (1961), 136-139.
[7] C. Casolo, Groups with all subgroups subnormal, Note di Mat., 28 (2) (2008), 1-149.
[8] G. Cutolo, On groups satisfying the maximal condition on non-normal subgroups, Riv. Mat. Pura 9 ( 1991), 49-59.
[9] G. Cutolo, L. A. Kurdachenko, Groups with a maximality condition for some non-normal subgroups, Geom. Dedicata, 55 (3) (1995), 279-292. [10] M. De Falco, L. A. Kurdachenko, I. Ya. Subbotin, Groups with only abnormal and subnormal subgroups, Atti Sem. Mat. Fis. Univ. Modena 46 (2) (1998), 435-442. [11] M. R. Dixon, L. A. Kurdachenko, I. Ya. Subbotin, On the structure of some contranormal-free groups, Comm. Algebra, 49 (11) (2021), 4940-4946. [12] M. R. Dixon, I. Ya. Subbotin, Groups with finiteness conditions on some subgroup system: a contemporary stage, Algebra Discrete Math, 4 (2009), 29-54. [13] G. Ebert, S. Bauman, A note on subnormal and abnormal chains, J. Algebra, 36 (2) (1975), 287-293.
[14] R. Esteban-Romero, G. Vincenzi, Some characterizations of groups in which normality is a transitive relation by means of subgroup embedding properties, Int. J. Group Theory, 7(2) (2018), 9-19. [15] R. Esteban-Romero, G. Vincenzi, On generalized FC-groups in which normality is a transitive relation, J. Aust. Math. Soc., 100 (2016), 192-198. [16] S. Franciosi, F. de Giovanni, On groups with many subnormal subgroups, Note Mat., 13 (1) (1993), 99-105.
[17] S. Franciosi, F. de Giovanni, Groups satisfying the minimal condition on non-subnormal subgroups, Infinite groups 1994 (Ravello), de Gruyter, Berlin (1996), 63-72. [18] W. Gaschütz, Gruppen in denen das Normalreilersein transitiv ist, J. Reine Angew. Math., 198 (1957), 87-92.
[19] G. Giordano, Gruppi con normalizzatori estremali, Matematiche (Catania), 26 (1971), 291-296 (1972).
[20] F. de Giovanni, G. Vincenzi, Groups satisfying the minimal condition on non-pronormal subgroups, Boll. Un. Mat. Ital. A, 9 (1) (1995), 185-194. [21] F. de Giovanni, G. Vincenzi, Pronormality in infinite groups, Math. Proc. R. Ir. Acad. 100A (2) (2000), 189-203.
[22] F. de Giovanni, G. Vincenzi, Pseudonormal subgroups of groups, Ricerche Mat. 52 (2003), 91-101.
[23] Yu. M. Gorchakov, On primitively factorized groups, Ukrainian Math. J., 14 (1962), 3-9.
[24] P. Hall, On the system normalizers of a soluble group, Proc. Lond. Math. Soc., 43 (1937), 507-528.
[25] H. Heineken, Groups with restriction on their infinite subnormal subgroups, Proc. Edinb. Math. Soc., 31 (1988), 231-241. [26] H. Heineken, J. C. Lennox, Subgroups of finite index in T-groups, Boll. Unione Mat. Ital., 134 (1985), 829-841.
[27] H. Heineken, A. Mohamed, A group with trivial centre satisfying the normalizer condition, J. Algebra, 10 (3) (1968), 368-376. [28] M. Herzog, P. Longobardi, M. Maj, A. Mann, On generalized Dedekind groups and Tarski Super Monsters, J. Algebra 226 (2) (2000), 690-713. [29] B. Huppert, Endliche Gruppen I, Springer-Verlag, Berlin-New York, 1967.
[30] V. V. Kirichenko, L. A. Kurdachenko, I. Ya. Subbotin, Some related to pronormality subgroup families and the properties of a group, Algebra Discrete Math., 11 (1) (2011), 75-108. [31] L. A. Kurdachenko, P. Longobardi, M. Maj, On the structure of some locally nilpotent groups without contranormal subgroups, J. Group Theory (2021), 000010151520210024, https://doi.org/10.1515/jgth-2021-0024. [32] L. A. Kurdachenko, J. Otal, On the influence of transitively normal subgroups on the structure of some infinite groups, Publ. Mat., 57 (1) (2013), 83 -106. [33] L. A. Kurdachenko, J. Otal, A. Russo, G. Vincenzi, Groups whose all subgroups are ascendant or self-normalizing, Cent. Eur. J. Math., 9 (2) (2011), 420-432. [34] L. A. Kurdachenko, J. Otal, I. Ya. Subbotin, On some criteria of nilpotency, Comm. Algebra, 30 (8) (2002), 3755-3776. [35] L. A. Kurdachenko, J. Otal, I. Ya. Subbotin, Abnormal, pronormal, contranormal and Carter subgroups in some generalized minimax groups, Comm. Algebra, 33 (12) (2005), 4595-4616. [36] L. A. Kurdachenko, J. Otal, I. Ya. Subbotin, Criteria of nilpotency and influence of contranormal subgroups on the structure of infinite groups, Turkish J. Math., 33 (2009), 227-237. [37] L. A. Kurdachenko, J. Otal, I. Ya. Subbotin, On influence of contranormal subgroups on the structure of infinite groups, Comm. Algebra, 37 (2010), 4542-4557. [38] L. A. Kurdachenko, A. A. Pypka, N. N. Semko, The groups whose cyclic subgroups are either ascendant or almost self-normalizing, Algebra Discrete Math., 21 (1) (2016), 111-127. [39] L. A. Kurdachenko, A. A. Pypka, I. Ya. Subbotin, On some properties of pronormal subgroups Cent. Eur. J. Math., 8 (5) (2010), 840-845. [40] L. A. Kurdachenko, A. A. Pypka, I. Ya. Subbotin, On the Structure of Groups Whose Non-normal Subgroups Are Core Free, Mediterr. J. Math., 16,136 (2019), 11 pp. https://doi.org/10.1007/s00009-019-1427-6. [41] L. A. Kurdachenko, A. Russo, G. Vincenzi, Groups without proper abnormal subgroups, J. Group Theory 9 (4) (2006), 507-518. [42] L. A. Kurdachenko, A. Russo, G. Vincenzi, On some groups all subgroups of which are near to pronormal, Ukrainian Math. J. 59 (2007), 1332-1339. [43] L. A. Kurdachenko, H. Smith, Groups with the maximal condition on non-subnormal subgroups, Boll. Un. Mat. Ital. B, 10 (2) (1996), 441-460. [44] L. A. Kurdachenko, H. Smith, Groups with the weak minimal condition for non-subnormal subgroups, Ann. Mat. Pura Appl., 173 (1997), 299-312. [45] L. A. Kurdachenko, H. Smith, Groups with the weak maximal condition for non-subnormal subgroups, Ricerche Mat., 47 (1) (1998), 29-49. [46] L. A. Kurdachenko, H. Smith, Groups in which all subgroups of infinite rank are subnormal, Glasg. Math. J., 46 (1) (2004), 83-89. [47] L. A. Kurdachenko, H. Smith, Groups with all subgroups either subnormal or self-normalizing, J. Pure Appl. Algebra, 196 (2-3) (2005), 271-278. [48] L. A. Kurdachenko, I. Ya. Subbotin, Pronormality, contranormality and generalized nilpotency in infinite groups, Publ. Mat., 47 (2) (2003), 389-414. [49] L. A. Kurdachenko, I. Ya. Subbotin, Transitivity of normality and pronormal subgroups, AMS Special session on infinite groups, October 8-9, 2005, Bard College, Combinatorial Group Theory, Discrete Groups, and Number Theory, A.M.S., Contemporary Mathematics, 421 (2006), 201-212. [50] N. F. Kuzennyi, I. Ya. Subbotin, Groups in which all subgroups are pronormal, Ukrainian Math. J., 39 (3) (1987), 325-329. [51] N. F. Kuzennyi, I. Ya. Subbotin, New characterization of locally nilpotent IH-groups, Ukrainian Math. J., 40 (1988), 274-277. [52] J. C. Lennox, S. E. Stonehewer, Subnormal subgroups of groups, Clarendon Press, Oxford, 1987.
[53] W. Möhres, Auflösbarkeit von Gruppen, deren Untergruppen alle subnormal sind, Arch. Math., 54 (1990), 232-235.
[54] T. A. Peng, Finite groups with pronormal subgroups, Proc. Amer. Math. Soc. 20 (1969), 232-234.
[55] T. A. Peng, Pronormality in finite groups, J. Lond. Math. Soc. 3 (2) (1971), 301-306.
[56] D. J. S. Robinson, Groups in which normality is a transitive relation, Proc. Cambridge Philos. Soc., 60 (1964), 21-38. [57] D. J. S. Robinson, A course in the theory of groups, Springer, New York, 1982.
[58] D. J. S. Robinson, A. Russo, G. Vincenzi, On groups which contain no HNN-extensions, Int. J. Algebra Comput., 17 (7) (2007), 1377 -1387. [59] J. S. Rose, Nilpotent subgroups of finite soluble groups, Math. Z., 106 (1968), 97- 112.
[60] A. Russo, On groups in which normality is a transitive relation, Comm. Algebra, 40 (2012), 3950-3954.
[61] R. Schmidt, Subgroups lattices of groups, Walter de Gruyter, Berlin, 1994.
[62] G. Vincenzi, Groups satisfying the maximal condition on non-pronormal subgroups, Algebra Colloq, 5 (1998), 121- 134. [63] G. Vincenzi, A characterization of soluble groups in which normality is a transitive relation, Int. J. Group Theory, 6 (2017), 21-27. [64] B. A. F. Wehrfritz, Groups with no proper contranormal subgroups, Publ. Mat., 64 (2020), 183-194.
[65] J. S. Wilson, On periodic generalized nilpotent groups, Bull. London Math. Soc., 9 (1977), 81-85.
[66] G. J. Wood, On pronormal subgroups of finite soluble groups, Arch. Math., 25 (1974), 578-585. | ||
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