可解群的一些充分条件

Some Sufficient Conditions of Soluble Groups

群G的一个子群H称为在G中S 正规的,如果存在G的一个次正规子群K,使得G=HK且H∩K G.该文利用π Hall子群和二极大子群的S 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 group G is said to be S-normal in G if there exists a subnormal subgroup K of G such that G=HK and HK is wubnormal in G. In this paper, the anthors give some sufficient conditions under which a group G is a soluble grouop by using S-normality of π-Hall subgroups, Sylow subgroups of odd order and second maximal subgroups of G.