完全条件置换子群对有限群结构的影响

Influence of completely conditionally permutable subgroups on the structure of finite groups

有限群G的子群H称为G的完全条件置换子群,如果对于G的任一子群K,存在x∈〈H,K〉,使得HKx=KxH.文中利用完全条件置换子群对有限群结构的影响,给出了超可解群的若干充分条件,并将一些结果进行了推广.

A subgroup H of a finite group G is said to be completely conditionally permutable in G if for every subgroup K of G,there exists an element x ∈ 〈H,K〉 such that HK^z=K^zH. Some sufficient conditions for a group to be supersoluble are obtained by using the influence of completely conditionally permutable subgroups on the structure of finite groups, and some results are generalized.