有限群可解的若干充分条件

Some Sufficient Conditions of Solvable Groups

称群G的一个子群H在G中弱拟c-正规,如果存在G的一个次正规子群K,使得H∩K为G的次正规子群,KH成群并且满足|G∶KH|为素数幂.利用子群的弱拟c-正规性给出了一个群为可解群的若干充分条件.

A subgroup H of a finite group G is said to be weakly quasi-c-normal in G if there exists a sub-normal subgroup K of G such that KH is a subgroup of G and ｜G∶KH｜ is a prime power.In this paper,the author gives some sufficient conditions for a finite group to be solvable.