具有弱正规性的有限群

FINITE GROUPS WITH WEAK NORMALITY

本文研究了一类有限可解MC-群G.若群G的任意非正规循环子群H,都存在一个素数p使得|G:H^G||p,则群G被称为MC-群.利用该群的可解性,获得了非幂零可解MC-群的详细分类.

In the paper,we study theˉnite soluble MC-groups.The group G is called an MC-group if there exists a prime p such that jG:HGj j p for each non-normal cyclic subgroup H of G.By using the solvability of G,we give the classiˉcation of theˉnite soluble non-nilpotent MC-groups.