幂零群的若干充分条件  

Some Sufficient Conditions of a Nilpotent Group

作　　者：管治安[1] 郭继东[1] 

机构地区：[1]伊犁师范学院数学系,新疆伊犁835000

出　　处：《甘肃联合大学学报（自然科学版）》2011年第5期25-26,28,共3页Journal of Gansu Lianhe University :Natural Sciences

基　　金：新疆维吾尔自治区自然科学基金资助项目(2010211A38)

摘　　要：利用完全条件置换子群的基本性质得到了:①如果G的每个素数阶元都是G的弱左Engle元,2∈π(G),G的每个4阶循环子群是G的完全条件置换子群,那么G幂零.②设N■G,G/N幂零,2∈π(G),若N的素数阶元均为G的弱左Engle元,N的每个4阶循环子群是G的完全条件置换子群,那么G幂零.③如果G的每个素数阶元x为NG(<x>)的弱左Engle元,<x>的每个4阶循环子群是G的完全条件置换子群,那么G幂零.Using some properties of complete conditional permutable subgroups,these results were obtained:①suppose every element with prime order of G is a weak left Engle element,2∈π(G),if every cyclic subgroup with order 4 is complete conditional permutable subgroups,then G is a nilpotent group.②suppose N■G,G/N is nilpotent,2∈π(G),if every cyclic subgroup of G with order 4 is complete conditional permutable subgroups,then G is a nilpotent group.③suppose every element x with prime order in G is weakly left Engle element in NG(<x>),if every cyclic subgroup of <x> with order 4 is complete conditional permutable subgroups,then G is a nilpotent group.

关 键 词：完全条件置换子群 有限群 幂零群 

分 类 号：O15[理学—数学]