广东工业大学学报 ›› 2012, Vol. 29 ›› Issue (3): 46-48.doi: 10.3969/j.issn.1007-7162.2012.03.008

• 综合研究 • 上一篇    下一篇

具有c1-可补子群的有限群结构分析

谭立辉,乔守红   

  1. 广东工业大学 应用数学学院，广东 广州 510006
  • 收稿日期:2012-02-28 出版日期:2012-09-20 发布日期:2012-09-20
  • 作者简介:谭立辉(1980-），女，讲师，博士，主要研究方向为数值分析、信号处理等.

Finite Groups with Some c1-Supplemented Subgroups

Tan Lihui,  Qiao Shouhong   

  1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou, 510006, China
  • Received:2012-02-28 Online:2012-09-20 Published:2012-09-20

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摘要： 子群H在群G中被称为是c1-可补的 (c1-supplemented), 如果存在G的子群K使得G=HK且H∩T≤Z∞(G)，其中Z∞(G)是G的超中心.本文研究素数幂阶子群的广义可补性对有限群结构的的影响，得到以下主要定理： 对于G的任意Sylowp-子群P， 如果P有子群D满足1<|D|<|P|且P每一个|D| 阶及p|D|阶子群在G中均c1-可补，那么G超可解.该结果推广了一些已知的结果.

关键词: 有限群；c1-可补子群；超可解群

Abstract: A subgroup H is called c1-supplemented in Gif there is a subgroup K such that G=HK and H∩T≤Z∞(G)，where Z∞(G) is the hypercenter of G. It investigates the influence of the c1-supplementation of subgroups on the structure of finite groups. The following results which generalize some related known results are obtained. Main Theorem: For any prime divisor p of |G|, let P be a Sylow p-subgroup of a group G. Suppose that P has a subgroup D satisfying the condition that 1<|D|<|P| and each subgroup of P of order |D|and p|D|is c1-supplemented in G. Then G is supersolvable.

Key words: finite groups；c1-supplemented subgroups；supersolvable groups

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