某些子群为SSH-子群的有限群

On Finite Groups of SSH-Subgroups

摘要: 设H是群G的一个子群，如果存在G的一个s-置换子群K,使得H^sG=HK并且对任意g∈G都有H^g∩N_K(H)≤H成立，则称H为G的SSH-子群。其中H^sG是G的包含着H的最小的s-置换子群。文章研究了具有素数幂阶SSH-子群的有限群的结构，给出了有限群为p-幂零群的一些刻画条件。

Abstract: Let G be a fnite group. A subgroup H of G is s-permutable in G if H permutes with every Sylow subgroup of G. A subgroup H of G is called an SSH-subgroup in G if G has an s-permutable subgroup K such that H^sG=HK and H^g∩N_K(H)≤H, for all g∈G,where H^sG is the intersection of all s-permutable subgroups of G containing H. This article studies the structure of fnite groups with SSH-subgroup which is prime power order. Some characterizations of a fnite group as a p-nilpotent group are given.