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- Title
Lower bounds on conjugacy classes of non-nilpotent subgroups in a finite group.
- Authors
Meng, Wei; Lu, Jiakuan
- Abstract
For a finite group G, let γ(G) denote the number of conjugacy classes of all non-nilpotent subgroups of G, and let π(G) denote the set of the prime divisors of |G|. In this paper, we establish lower bounds on γ(G). In fact, we show that if G is a finite solvable group, then γ(G) = 0 or γ(G) ≥ 2|π(G)|-2, and if G is non-solvable, then γ(G) ≥ |π(G)| + 1. Both lower bounds are best possible.
- Subjects
FINITE groups; CONJUGACY classes; NILPOTENT groups; SOLVABLE groups; SET theory
- Publication
Journal of Algebra & Its Applications, 2015, Vol 14, Issue 3, p-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498815500395