弱NS*-置换子群对有限群超可解的影响

The Effects of Weakly NS*-Permutable Subgroups on the Supersolvability of Finite Groups

摘要: 设G是有限群，H是G的一个子群。称H是G的几乎S-置换子群，若H≤K≤G且对于（p,|H|）=1的任意素数p，使得正规化子N_K（H）包含K的某些Sylow p-子群。称H是G的弱NS*-置换子群，若存在G的一个次正规子群T，使得HT=G且H∩T≤H_nG，其中H_nG由包含在H中的所有几乎S-置换子群生成。本文假设G的某些子群是弱NS*-置换子群的前提下，得到G的相关结构定理。

Abstract: Let G be a finite group. A subgroup H of G is called nearly S-permutable subgroup in G if for every prime p with （p,|H|）=1 and for every subgroup K of G containing H the normalizer N_K（H） contains some Sylow p-subgroup of K. A subgroup H of G is said to be weakly NS* -permutable sub-group of G if there exists a subnormal T of G such that G = HT, and H∩T≤H_nG, where H_nG is the subgroup of H generated by all those subgroups of H which are nearly S-permutable in G. In this article, we investigate the structure of G under the assumption that some subgroups are weakly NS*-permutable subgroups of G.