局部化的M-可补子群对群构造的影响

吉林大学学报(理学版)

局部化的M-可补子群对群构造的影响

高百俊^1，张佳²

1. 伊犁师范学院数学与统计学院, 新疆伊宁 835000; 2. 西华师范大学数学与信息学院，四川南充 637009

收稿日期:2016-12-26 出版日期:2017-11-26 发布日期:2017-11-29
通讯作者: 高百俊 E-mail:dqgbj2008@163.com

Influence of Localized M-SupplementedSubgroups on Structure of Finite Groups

GAO Baijun¹, ZHANG Jia²

1. School of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang Uygur Autonomous Region, China;
2. School of Mathematics and Information, China West Normal University, Nanchong 637009, Sichuan Province, China

Received:2016-12-26 Online:2017-11-26 Published:2017-11-29
Contact: GAO Baijun E-mail:dqgbj2008@163.com

摘要/Abstract

摘要： 假设群G的一个Sylow p-子群P的子群D满足1G(P)中的M-可补性质, 并结合
H(P)={H≤P|P′≤H≤Φ(P)}中子群的弱s-可补性质, 得到了刻画p-幂零群和p-超可解群新的充分条件.

关键词: Sylow p-子群, 弱s-可补子群, M-可补子群, 正规化子

Abstract: We supposed that a subgroup D of a Sylow p-subgroup P of a group G satisfied 1<D≤P, where p was a prime divisor of |G|. The new sufficient conditions for the characterization of p-nilpotent groups and p-supersolvable groups were obtained by using Msupplemented property of each order of |D| subgroup in the normalizer N_G(P) of P and combining the weakly ssupplemented property of H (P)={H
≤P|P′≤H≤Φ(P)}.

Key words: normalizer, weakly s-supplemented subgroup, Sylow p-subgroup, supplemented subgroup

中图分类号:

O152.1

高百俊，张佳. 局部化的M-可补子群对群构造的影响[J]. 吉林大学学报(理学版), 2017, 55(06): 1469-1472.

GAO Baijun, ZHANG Jia. Influence of Localized M-SupplementedSubgroups on Structure of Finite Groups[J]. Journal of Jilin University Science Edition, 2017, 55(06): 1469-1472.