CS-拟正规子群对有限群结构的影响

The Influence of CS-quasinormality of Some Subgroups on the Structure of Finite Groups

H是有限群G的子群,若G中存在S-拟正元规子群T,使得G=HT且T∩H在G中S-拟正规,则称H在G中GS-拟正元规,设P是G的非循环Sylow子群,D满足1<|D|<|P|,若P中所有阶与|D|相等的子群H在G中没有超可解补,则H在G中CS-拟正规.

Consider H as a finite subgroup of G, some finite group. H is CS-quasinormal in G if G has an S-quasinormal subgroup T such that HT = G and T = ∩ H is S-quasinormal in G. Given P is a noncyclic Sylowsubgroup of G and one subgroup D meets 1 〈 ｜ D ｜ 〈 ｜P ｜ , and if H has no supersolvable supplement in G under the assumption that all subgroups H of P has the same order as D, His CS-quasinormal in G.