关于有限群子群的弱S-可补性

The Weakly s-Supplemented Property of Finite Groups

设G是一个有限群,H是G的一个子群.称H为G的一个s-置换子群,若对于G的任意Sylow子群P,成立HP=PH.称H为G的一个弱s-可补的子群.若存在G的一个子群T,使得G=HT且H∩T≤H_s G,其中H_s G是包含在H中的G的最大的s-置换子群.本文在假设G的某些子群是弱s-可补的前提下,得到了G的一个结构定理,并推广了许多近期的结果.

Suppose that G is a finite group and H is a subgroup of G.H is said to be s-permutable in G if HP = PH for any Sylow subgroup P of G.H is said to be weakly s-supplemented in G if there is a subgroup T of G,such that G = HT and H ∩ T ≤ H_s G,where H_b g is the biggest s-permutable subgroup of G contained in H.In this paper,a structural theorem of finite groups is given under the hypothesis that some subgroups of G are weakly s-supplemented subgroups of G.Many recent results are extended.