关于有限群的c-正规性的几点注记

关于有限群的c-正规性的几点注记

刘晓蕾

山西财经大学应用数学系, 山西太原 030006

收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2006-10-24 发布日期:2006-10-24
通讯作者: 刘晓蕾

On generalized c-normality of finite groups

LIU Xiao-lei

Department of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, Shanxi, China

Received:1900-01-01 Revised:1900-01-01 Online:2006-10-24 Published:2006-10-24
Contact: LIU Xiao-lei

摘要/Abstract

摘要：

推广了有限群中的c-正规性概念,引入了c-次正规性和c-π-拟正规性概念, 并利用新概念给出了有限群可解的几个条件,证明了:设G是有限群，那么,下述条件是等价的:(ⅰ) G有一个极大子群M在G中是c-π-拟正规的而且是可解的。 (ⅱ) G的每一个具有复合指数的极大子群在G中是c-π-拟正规的。 (ⅲ) G的每一个极大子群在G中是c-次正规的。 (ⅳ) G是可解的。

关键词: 有限群, c-π-拟正规性, c-次正规性

Abstract:

For a finite group G, a subgroup H is called c-normal in G if there is a normal subgroup K such that G=HK and H∩K≤HG, the largest normal subgroup of G contained in H. c-normality was replaced by c-π-quasinormality or c-sub-normality. The following were showed equivalent. First, there is a solvable maximal subgroup M such that M is c-π-quasi-normal in G.Second, every maximal subgroup with composite index of G is c-π-quasi-normal in G. Third, every maximal subgroup of G is c-subnormal in G. Fourth, G is solvable.

Key words: c-π-quasinormality

, c-subnormality,

finite groups

中图分类号:

O152

刘晓蕾 . 关于有限群的c-正规性的几点注记[J]. J4, 2008, 43(10): 18-20 .

LIU Xiao-lei . On generalized c-normality of finite groups[J]. J4, 2008, 43(10): 18-20 .

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