弱c^(##)-正规子群及其性质  

On Weak c^(##)-Normality and Its Properties

作　　者：殷维莹 郭继东[1] 

机构地区：[1]伊犁师范学院数学与统计学院,新疆伊宁835000

出　　处：《伊犁师范学院学报（自然科学版）》2013年第4期21-23,共3页Journal of Yili Normal University：Natural Science Edition

基　　金：新疆维吾尔自治区普通高等学校重点学科开放课题(2012ZDXK06)

摘　　要：利用弱c##--正规子群研究有限群的幂零性,得出以下结论:①设G是群,H≤G,若H在G中弱c##-正规且H≤M≤G,则H在M中弱c##-正规.②设π为素数集,H是G的π-子群,N为G的正规π'-子群,如果H在G中弱c##-正规,则HN/N在G/N中弱c##-正规.③设G的每个素数阶元均为G的弱左Engle元,若2∈π(G),且G的每个4阶循环子群均在G中弱c##-正规,则G是幂零群.④设NΔG,G/N为幂零的,且2∈π(G).若N的每个素数阶元均为G的弱左Engle元,且N的每个4阶循环子群也在G中弱c##-正规,则G是幂零群.The influence of Weakly ##c -normal Subgroup on the nilpotency of finite groups is investigated.①Suppose that G is a finite group, H ≤G , if H is weakly ##c -normal in G , and H ≤M ≤G , then H is weakly ##c -normal in M . ②Suppose that πis a prime set, H is a π-subgroup of G , N is a normalπ′-subgroup of G , if H is weakly ##c -normal in G , then HN/N is weakly ##c -normal in G/N .③Suppose that x is a weakly left Engle element for every element x of G with prime order, 2∈π（G） , if x is weakly ##c -normal in G for every element x of G with order 4, then G is nilpotent. ④ Suppose that N〈G , G/N is nilpotent, 2∈π（G） . If x is a weakly left Engle element for every element x of N with prime order, and x is weakly ##c -normal in G for every element x of N with order 4, then G is nilpotent.

关 键 词：弱c##-正规子群 幂零群 弱左Engle元 

分 类 号：O152.1[理学—数学]