Finite groups with some non-Abelian subgroups of non-prime-power order |
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Authors: | Wei Meng Hailou Yao |
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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 |
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Abstract: | Let G be a finite group and NA(G) denote the number of conjugacy classes of all nonabelian subgroups of non-prime-power order of G. The Symbol π(G) denote the set of the prime divisors of |G|. In this paper we establish lower bounds on NA(G). In fact, we show that if G is a finite solvable group, then NA(G) = 0 or NA(G) ≥ 2|π(G)|?2, and if G is non-solvable, then NA(G) ≥ |π(G)| + 1. Both lower bounds are best possible. |
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