完全C-置换子群

Completely C-permutable subgroups

群G的一个子群H称在G中完全条件置换(或完全C-置换).如果对群G的任意子群K,存在x∈〈H,K〉,满足HKx=KxH.利用子群的完全C-置换性给出了群为p-幂零群及超可解群的一些特征.

A subgroup H of a group G is said to be completely conditionally permutable（or in brevitv. completely c-permutable） in G if for every subgroup T of G there exists an element x ∈〈 H, T〉 such that HT^x = T^xH. This paper analyses the characteristics of p-nilpotent group and supersovable group with completely e-permutable subgroups.