某些子群为置换嵌入的有限群(英文)

有限群G的子群H称为它的置换子群，如果H对G的每个子群置换．群G的子群K称为G的置换嵌入子群，如果对K的任意素因子P，K的Sylow P子群是G的某个置换子群的SylowP子群．利用置换嵌入子群得到了P幂零群的一个判别定理以及在一个给定群系下有关群的一些结构．

Finite groups in which certain subgroups are permutably embedded

A subgroup H of a finite group G is said to be permutable in G if it permutes with every subgroup of G.A subgroup K of a finite group G is said to be permutably embedded in G if for each prime p dividing the order of K,a Sylow p-subgroup of K is also a Sylow p-subgroup of some permutable subgroup of G.In this paper we give a criterion for a group G to be supersolvable,in terms of permutably embedded subgroups of a finite group G.