Finite Groups with Some c<sub>1</sub>-Supplemented Subgroups

Tan Li-hui; Qiao Shou-hong

doi:10.3969/j.issn.1007-7162.2012.03.008

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Finite Groups with Some c₁-Supplemented Subgroups

更新时间：2026-05-27

- Finite Groups with Some c₁-Supplemented Subgroups
- Vol. 29, Issue 3, Pages: 46-48(2012)
- 作者机构：
- 作者简介：
- 基金信息：
- DOI：10.3969/j.issn.1007-7162.2012.03.008
  CLC：
- Online First：20 September 2012，
  
  Published：2012
- 稿件说明：
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谭立辉, 乔守红. 具有c₁-可补子群的有限群结构分析[J]. 广东工业大学学报, 2012, 29(3): 46-48. DOI: 10.3969/j.issn.1007-7162.2012.03.008.

Tan Li-hui, Qiao Shou-hong. Finite Groups with Some c₁-Supplemented Subgroups[J]. 2012, 29(3): 46-48. DOI: 10.3969/j.issn.1007-7162.2012.03.008.
谭立辉, 乔守红. 具有c₁-可补子群的有限群结构分析[J]. 广东工业大学学报, 2012, 29(3): 46-48. DOI: 10.3969/j.issn.1007-7162.2012.03.008. DOI：

Tan Li-hui, Qiao Shou-hong. Finite Groups with Some c₁-Supplemented Subgroups[J]. 2012, 29(3): 46-48. DOI: 10.3969/j.issn.1007-7162.2012.03.008. DOI：

摘要

子群

在群

中被称为是c

-可补的 (c

-supplemented)

如果存在

的子群

使得

且

∩

≤

∞

(

)，其中

∞

(

)是

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

的任意Sylow

-子群

，如果

有子群

满足1

|且

每一个|

| 阶及

|阶子群在

中均c

-可补，那么

超可解.该结果推广了一些已知的结果.

Abstract

A subgroup

is called c

-supplemented in

if there is a subgroup

such that

G=HK

and

∩

≤

∞

(

)，where

∞

(

) is the hypercenter of

. It investigates the influence of the c

-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

of |

let

be a Sylow

subgroup of a group

. Suppose that P has a subgroup

satisfying the condition that 1

| and each s

ubgroup of P of order |

|and

|is c

-supplemented in

. Then

is supersolvable.

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Related Author

QIAO Shou-Hong

GUO Da-Chang

Qiu Zheng-tian

Qiao Shou-hong

Related Institution

School of Applied Mathematics, Guangdong University of Technology

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Finite Groups with Some c1-Supplemented Subgroups

DOI：10.3969/j.issn.1007-7162.2012.03.008

摘要

Abstract

关键词

Keywords

references

Finite Groups with Some c₁-Supplemented Subgroups