子群的半覆盖—避开性与有限群的结构

设G是有限群,H为G的子群.如果存在一个主群列1=G_0(?)G_1(?)…(?) G_(n-1)(?)G_n=G,使得对每个i=1,2,…,n,或者H覆盖G_i/G_(i-1),或者H避开G_i/G_(i-1),则称H为G的半覆盖—避开子群.利用G的Sylow子群的极大子群,Sylow子群的2-极大子群的半覆盖—避开性得到了群的可解性,p-幂零性的判别,同时得到了群系的一些结论.     

S-半正规性与P-幂零性

In this paper, we deal mainly with the following problem: if every 2-maximal subgroup of a Sylow p-subgroup of a finite group G is S-seminormal in G, what conditions force G to be p-nilpotent? As an application of main results, some sufficient conditions for finite nilpotent groups and finite supersolvable groups are obtained.     

On s-Permutable Subgroups and p-Nilpotency of Finite Groups

A subgroup H of a finite group G is said to be s-permutable in G if H permutes with every Sylow subgroup of G. In this article, some sufficient conditions for a finite group G to be p-nilpotent are given whenever all subgroups with order p ^m of a Sylow p-subgroup of G are s-permutable for a given positive integer m.