完全条件置换子群对有限群结构的影响

Influences of Completely Conditionally Permutable Subgroups on the Structure of Finite Groups

群G的子群H称为在G中完全条件置换的,如果对于G的每个子群K,都存在x∈〈H,K〉,使得HKx=KxH.本文利用子群的完全条件置换性来讨论有限群的结构,得到了有限群为超可解群,p-幂零群的充分条件.

A subgroup H of a group G is said to be completely conditionally permutable in G if forevery subgroup k of G. There exists an element x ∈〈H , K） such that HK^z = K^zH. In this paper the structures of finite groups are discussed by means of the completely conditionally permutability of some subgroups, some sufficient conditions for a finite group to be supersolvable orp- nilpotent are obtained.