Finite groups with some non-Abelian subgroups of non-prime-power order

Wei Meng () and Hailou Yao ()
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Wei Meng: Beijing University of Technology
Hailou Yao: Beijing University of Technology

Indian Journal of Pure and Applied Mathematics, 2016, vol. 47, issue 4, 733-739

Abstract: 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.

Keywords: Non-abelian subgroup; conjugacy class; solvable group (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s13226-016-0212-5

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