关于S-拟正规性的一些必要条件

Several necessary conditions of S-quasinormal subgroup

为证明S-拟正规子群是否具有半正规性,并应用有限群的子集的S-拟正规性来研究有限群的超可解性.设G为有限群,H≤G,称H为G的S-拟正规子群,如果对于G的任意一个Sylow子群P,都有HP=PH.给有限群的某些子集赋予S-拟正规性。

To prove whether S-quasinormal subgroups have half normality , and using S-quasinormality of subset to study the supersolvablity in finite group .Let G be a finite group . A subgroup H of G is said to be S-quasinormal in G if HP=PH for all Sylow subgroups P of G.Let several subsets in finite group have S-quasinormal, which could get the result that the group have supersolvablity .