准素数子群的δ-置换性对有限群结构的影响

The influence ofδ-permutability of primary subgroups on the structure of finite groups

设δ是有限群的Sylow子群的完全集,即对每一个|G|的素因子p,δ仅包含G的一个Sylow p-子群.有限群G的子群H称为δ-置换的,若H置换δ中的每个元素.讨论δ-置换子群对有限群结构的影响,并推广一些已有的结论.

Letδbe a complete set of Sylow subgroups of G,that is,for each prime p dividing the order of G,δcontained exactly one and only one Sylow p-subgroup of G.A subgroup H of a finite group G was said to beδ-permutable if H permuted with every member ofδ.In this paper,we investigated the influence ofδ-permutable subgroups on the structure of finite groups.