关于弱s-置换嵌入子群的几个定理

Some Theorems on Weakly s-Permutably Embedded Subgroups

称群G的一个子群H在G中弱s-置换嵌入的,如果存在G的一个次正规子群T和包含在H中的G的一个s-置换嵌入子群Hse使得G=HT且H∩T≤Hse。利用弱s-置换嵌入子群的性质给出了p-幂零群和p-超可解的一些新刻画。

A subgroup H of a group G is believed to be weakly s-permutably embedded in G if there are a subnormal subgroup T of G and an s-permutably embedded subgroup Hse of G contained in H such that G=HT and H∩T≤ Hse.By using the property of weakly s-permutably embedded groups,some new criterions of p-nilpotency and p-supersolvability of finite groups are obtained.