弱-可补子群对有限群结构的影响

Journal of Guangxi Normal University(Natural Science Edition) ›› 2012, Vol. 30 ›› Issue (1): 25-28.

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Influence of Weakly -supplemented Subgroups on theStructure of Finite Groups

LI Xian-chong¹, LI Xian-hua²

1.School of Mathematics and Computer Science,Guizhou Normal University,Guiyang Guizhou 550001,China;
2.School of Mathematical Science,Soochow University,Suzhou Jiangsu 215006,China

Received:2011-11-26 Online:2012-01-20 Published:2018-12-03

Abstract

Abstract: Let H be a subgroup of a finite group G.H iscalled weakly -supplemented if there exists a subgroup T of Gsuch that G=TH and H∩T≤H_G,where H_G is the subgroup generalized by all subgroups of H which are s-semipermutablein G.In this paper,the influence of minimal subgroups and subgroups of order 4 which are weakly -supplemented in G on the structure of finite groups is studied,and several sufficient conditions of p-nilpotency of G are given.

Key words: weakly -supplemented subgroups, p-nilpotent group, minimal subgroup

CLC Number:

O152.1

LI Xian-chong, LI Xian-hua. Influence of Weakly -supplemented Subgroups on theStructure of Finite Groups[J].Journal of Guangxi Normal University(Natural Science Edition), 2012, 30(1): 25-28.

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