有限群的弱s-可换嵌入子群(英文)

On finite groups with some weakly s-permutably embedded subgroups

设H为群G的一个子群,如果存在G的次正规子群T和群G的一个包含在H中的弱s-可换嵌入子群Hse使得G=HT且H∩T≤Hse,则称H为群G的一个弱s-可换嵌入子群.我们研究了弱s-可换嵌入子群对有限群的p-超可解性和p-幂零性的影响.推广了一些已有的结果.

A subgroup H of a group G is said 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.In this paper,we investigate the influence of weakly s-permutably embedded subgroups on the p-supersolvability and p-nilpotency of finite groups.Some earlier results are generalized.