具有给定阶c-正规子群的有限群

Finite groups with given c-normal subgroups

设H是群G的子群,如果G中存在正规子群K,使得G=HK且H∩K≤HG,那么称H在G中c-正规.对于p-可解群G,其中p是|G|的素因子,如果Fp(G)的任意指数为p的极大子群在G中c-正规,那么G是p-超可解的.

A subgroup H of G is called c-normal in G if there exists a normal subgroup K such that G=HK and H∩K≤HG. For a p-solvable group G, where p is a prime divisor of ｜G｜, if every maximal subgroup of Fp（G） with index p is c-normal in G, then G is p-supersolvable.