A note on the conjugacy classes of non-cyclic subgroups |
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| Authors: | Wei Meng Hailou Yao Li Ma |
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| Institution: | 1. College of Applied Sciences, Beijing University of Technology, Beijing, P. R. China;2. School of Mathematics and Computer Sciences, Yunnan Minzu University, Kunming, Yunnan, P. R. China;3. School of Mathematics and Statistics, Qujing Normal University, Qujing, Yunnan, P. R. China |
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| Abstract: | Let G be a finite group and δ(G) denote the number of conjugacy classes of all non-cyclic subgroups of G. The symbol π(G) denotes the set of the prime divisors of |G|. In 7 Meng, W., Li, S. R. (2014). Finite groups with few conjugacy classes of non-cyclic subgroups. Scientia Sin. Math. 44:939–944.Crossref] , Google Scholar]], Meng and Li showed the inequality δ(G)≥2|π(G)|?2, where G is non-cyclic solvable group. In this paper, we describe the finite groups G such that δ(G) = 2|π(G)|?2. Another aim of this paper would show δ(G)≥M(G)+2 for unsolvable groups G and the equality holds ?G?A5 or SL(2,5), where M(G) denotes the number of conjugacy classes of all maximal subgroups of G. |
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| Keywords: | Conjugacy class cyclic subgroups maximal groups |
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