The influence of CAP*-subgroups on the solvability of finite groups

Liu Jianjun; Guo Xiuyun; Li Shirong

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The influence of CAP*-subgroups on the solvability of finite groups

Liu Jianjun 1,Guo Xiuyun 1 #,Li Shirong 2

1.Shanghai University

2.Department of Mathematics, Guangxi University

*Correspondence author

#Submitted by

Subject:

Funding: 国家自然科学基金,教育部博士点基金,上海市教委重点学科（No.10771132,200802800011,J50101）

Opened online: 2 April 2010

Accepted by: none

Citation: Liu Jianjun ,Guo Xiuyun ,Li Shirong.The influence of CAP*-subgroups on the solvability of finite groups[OL]. [ 2 April 2010] http://en.paper.edu.cn/en_releasepaper/content/41494

A subgroup H of a group G is said to be a CAP*-subgroup of a group G if, for any non-Frattini chief factor K/L of G, we have HK=HL or H∩K=H∩L. In this paper, some new characterizations for finite solvable groups are obtained based on the assumption that some subgroups are CAP*-subgroups of G.

Keywords:Frattini chief factor;solvable group;cover-avoiding property

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