Finite groups with some CAP-subgroups

Jianjun Liu (), Shirong Li, Zhengcai Shen and Xiaochun Liu
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Jianjun Liu: Shanghai University
Shirong Li: Guangxi University
Zhengcai Shen: Suzhou University
Xiaochun Liu: Guangxi University

Indian Journal of Pure and Applied Mathematics, 2011, vol. 42, issue 3, 145-156

Abstract: Abstract Let G be a finite group. A subgroup H of G is called a CAP-subgroup if the following condition is satisfied: for each chief factor K/L of G either HK = HL or H ∩ K = H ∩ L. Let p be a prime factor of |G| and let P be a Sylow p-subgroup of G. If d is the minimum number of generators of P then there exists a family of maximal subgroups of P, denoted by M d (P)={P 1, P 2,…, P d } such that ∩ i=1 d P i = ϕ(P). In this paper, we investigate the group G satisfying the condition: every member of a fixed M d (P) is a CAP-subgroup of G. For example, if, in addition, G is p-solvable, then G is p-supersolvable.

Keywords: Cover-avoidance properties; P-supersolvable groups; p-nilpotent groups; supersolvable groups (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s13226-011-0009-5

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