s-半置换子群对群的幂零性的影响  

Influences of s-semipermutablility of Subgroups on p-nilpotence of Finite Groups

作　　者：王丽芳[1] 

机构地区：[1]山西师范大学数学与计算机科学学院,山西临汾041004

出　　处：《山西师范大学学报（自然科学版）》2006年第4期6-9,共4页Journal of Shanxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(10471085);山西省自然科学基金(20051007);山西省回国留学人员基金(晋留管办(2004)7号)

摘　　要：群G的子群H称为半置换的,若对任意的K≤G,只要(|H|,|K|)=1,就有HK=KH,H称为s-半置换的,若对任意的p‖G|,只要(p,|H|)=1,就有PH=HP,其中P∈Sylp(G).本文利用极小子群的s-半置换性得到幂零群的若干充分条件.A subgroup H of a group G is called semipermutable if it is permutable with every subgroup K of G with(|H|,|K|)=1,and s-semipermutable if it is permutable with every Sylow p-subgroup of G with((p,|H|))=1.With s-semipermutability of the minimal subgroups,some sufficient conditions of p-nilpotent and nilpotent group are obtained in this paper.

关 键 词：S-半置换子群 p-幂零群:幂零群 

分 类 号：O152.1[理学—数学]