CSS-拟正规子群与有限群的超可解性

CSS-Quasinormal Subgroups and Supersolvability of Finite Groups

群G的一个子群H称为在G中CSS-拟正规的,如果存在G的拟正规子群T,使得G=HT,且H∩T是G的SS-拟正规子群。文章通过讨论某些素数幂阶CSS-拟正规子群与有限群的超可解性,推广了有关文献的一些结果。

A subgroup H of a finite group G is said to be CSS-quasinormal in G if there exists a quasinormal subgroup T of G such that G=HT and H∩T is SS-quasinormal in G.In this paper,we investigate the supersolvability of a group G under the assumption that certain subgroups of prime power order are CSS-quasinormal in G.The results obtained generalized some known works in the literatures.