华东师范大学学报（自然科学版） >

2019 , Vol. 2019 >Issue 2: 63 - 68

DOI: https://doi.org/10.3969/j.issn.1000-5641.2019.02.007

数学

具有Mp-可补子群的有限群的局部化定理

  • 鲍宏伟 ,
  • 李凤清 ,
  • 张佳 ,
  • 汤菊萍
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  • 1. 蚌埠学院 理学院, 安徽 蚌埠 233030;
    2. 四川职业技术学院, 四川 遂宁 629000;
    3. 西华师范大学 数学与信息学院, 四川 南充 637009;
    4. 无锡职业技术学院, 江苏 无锡 214121
鲍宏伟,男,副教授,研究方向为有限群论.E-mail:big_bao2003@163.com.

收稿日期: 2018-02-02

  网络出版日期: 2019-03-27

基金资助

国家自然科学基金（11701223）；安徽省高校自然科学基金（KJ2017A569）；西华师范大学博士科研启动项目（17E091）；西华师范大学基本科研业务费项目（18B032）

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Localized theorems of finite groups with Mp-supplemented subgroups

  • BAO Hong-wei ,
  • LI Feng-qing ,
  • ZHANG Jia ,
  • TANG Ju-ping
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  • 1. Faculty of Science, Bengbu University, Bengbu Anhui 233030, China;
    2. Sichuan Vocational and Technical College, Suining Sichuan 629000, China;
    3. School of Mathematics and Information, China West Normal University, Nanchong Sichuan 637009, China;
    4. Wuxi Institute of Technology, Wuxi Jiangsu 214121, China

Received date: 2018-02-02

  Online published: 2019-03-27

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摘要

已知H是群G的子群，如果存在G的子群B，使得G=HB且对于H的满足|H：T|=pα的任意极大子群T，有TB<G，则称子群H在G中是Mp-可补的.结合局部化思想，利用子群的Mp-可补性质研究有限群的构造，得到了p-幂零群和p-超可解群的若干充分条件.

关键词： Mp-可补子群; Sylow子群; 有限群

本文引用格式

鲍宏伟 , 李凤清 , 张佳 , 汤菊萍 . 具有Mp-可补子群的有限群的局部化定理[J]. 华东师范大学学报（自然科学版）, 2019 , 2019(2) : 63 -68 . DOI: 10.3969/j.issn.1000-5641.2019.02.007

Abstract

A subgroup H of G is Mp-supplemented in G, if there exists a subgroup B of G such that G=HB and TB < G for every maximal subgroup T of H with|H:T|=pα. Based on the idea of localization, by using the Mp-supplemented properties of some primary subgroups to study the structure of finite groups, we obtained sufficient conditions for p-nilpotent and p-supersolvable groups.

Key words： Mp-supplemented subgroup; Sylow subgroup; finite group

参考文献

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