On large proportions of cyclic subgroups in finite group

Gao, Xiaofang; Shen, Rulin

doi:10.22108/ijgt.2026.148673.2019

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	On large proportions of cyclic subgroups in finite group
International Journal of Group Theory
مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 16 آبان 1405 اصل مقاله (470.14 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2026.148673.2019
نویسندگان
Xiaofang Gao¹؛ Rulin Shen^* ²
¹School of Mathematics and Statistics, Hubei University, Wuhan 430062, Hubei, China
²Department of Mathematics, Hubei Minzu University, Enshi 445000, Hubei, China
چکیده
Let $c(G)$ be the number of cyclic subgroups of the finite group $G$ and $\alpha(G)$ the function $c(G)/\|G\|$. In this paper, we classify the non $2$-groups with $17/24\leq \alpha(G)<3/4$.
کلیدواژه‌ها
Supersolvable groups؛ Number of cyclic subgroups؛ Non $2$-groups

مراجع
[1] G. A. Miller, On the number of cyclic subgroups of a group, Proc. Natl. Acad. Sci. U.S.A., 15 no. 9 (1929) 728–731. [2] G. A. Miller, Determination of all the groups of order 2m which contain an odd number of cyclic subgroups of composite order, Trans. Amer. Math. Soc., 6 no. 1 (1905) 58–62. [3] I. M. Richards, A remark on the number of cyclic subgroups of a finite group, Amer. Math. Monthly, 91 no. 9 (1984) 571–572. [4] W. Meng and J. Lu, Lower bounds on the number of cyclic subgroups in finite non-cyclic nilpotent groups, J. Math. Study, 56 no. 1 (2023) 93–102. [5] L. T´oth, On the number of cyclic subgroups of a finite abelian group, Bull. Math. Soc. Sci. Math. Roumanie (N.S.), 55(103) no. 4 (2012) 423–428. [6] M. Tˇarnˇauceanu, Finite groups with a certain number of cyclic subgroups, Amer. Math. Monthly, 122 no. 3 (2015) 275–276. [7] M. Tˇarnˇauceanu, Finite groups with a certain number of cyclic subgroups II, Acta Univ. Sapientiae Math., 10 no. 2 (2018) 375–377. [8] R. Belshoff, J. Dillstrom and L. Reid, Finite groups with a prescribed number of cyclic subgroups, Comm. Algebra, 47 no. 3 (2019) 1043–1056. [9] R. Belshoff, J. Dillstrom and L. Reid, Addendum to “Finite groups with a prescribed number of cyclic subgroups”, Comm. Algebra, 47 no. 10 (2019) 3939–3940. [10] E. Haghi and A. R. Ashrafi, On the number of cyclic subgroups in a finite group, Southeast Asian Bull. Math., 42 (2018) 865–873. [11] A. R. Ashrafi and E. Haghi, On n-cyclic groups, Bull. Malays. Math. Sci. Soc., 42 (2019) 3233–3246. [12] K. Sharma and A. S. Reddy, Groups having 11 cyclic subgroups, Int. J. Group Theory, 13 no. 2 (2024) 203–214. [13] K. Sharma and A. S. Reddy, Groups having 12 cyclic subgroups, Bull. Aust. Math. Soc., 113 no. 2 (2026) 304–315. [14] M. Garonzi and I. Lima, On the number of cyclic subgroups of a finite group, Bull. Braz. Math. Soc. (N.S.), 49 no. 3 (2018) 515–530. [15] R. Shen and X. Gao, The finite groups with many cyclic subgroups, Indian J. Pure Appl. Math., 54 (2023) 485–498. [16] The GAP Group, GAP-Groups, algorithms, and programming, Version 4.7.8. [17] C. T. C. Wall, On groups consisting mostly of involutions, Math. Proc. Cambridge Philos. Soc., 67 no. 2 (1970) 251–262. [18] H. Kurzweil and B. Stellmacher, The theory of finite groups: an introduction, Springer, Berlin, 2004. [19] L. E. Dickson, Linear groups: With an exposition of the Galois field theory, With an introduction by W. Magnus. Dover Publications, Inc., New York, 1958.
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On large proportions of cyclic subgroups in finite group