几乎SS-嵌入子群对有限群p-幂零性的影响

doi:10.16088/j.issn.1001-6600.2019.01.017

Abstract

Abstract: A subgroup H is said to be nearly SS-embedded in a finite group G if there exists an s-permutable subgroup T of G such that HT is s-permutable in G and H∩T≤H_seG,where H_seG is the subgroup contained in H,generated by all those subgroups of H which are s-permutably embedded in G. Let M_d(P)={P₁,P₂,…,P_d} be a set of the maximal subgroups of a group P of prime power order such that ∩^d_i=1P_i=Φ(P). The influence of the set M_d(P) with the above property on the p-nilpotency of finite groups is investigated, and some recent related results are generalized.

Key words: finite group, s-permutable subgroup, s-permutably embedded subgroup, nearly SS-embedded subgroup, p-nilpotent group

CLC Number:

O152.1

LÜ Yubo, WEI Huaquan, LI Min. The Influence of Nearly SS-embedded Subgroups on the p-nilpotency of Finite Groups[J].Journal of Guangxi Normal University(Natural Science Edition), 2019, 37(1): 149-154.

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