非正规子群共轭类类数为2的有限群的一个注记

非正规子群共轭类类数为2的有限群的一个注记

陈顺民¹,², 陈贵云³

1. 陕西师范大学数学与信息科学学院, 西安 710062； 2. 重庆文理学院数计系, 重庆 402160;3. 西南大学数学与统计学院, 重庆 400715

收稿日期:2007-12-10 修回日期:1900-01-01 出版日期:2008-11-26 发布日期:2008-11-26
通讯作者: 陈贵云

A Note on Finite Groups Having Exactly Two Conjugacy Classesof Nonnormal Subgroups

CHEN Shunmin¹,², CHEN Guiyun³

1. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China；2. Department of Mathematics and Computer Science, Chongqing University of Arts and Sciences, Chongqing 402160, China;3. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Received:2007-12-10 Revised:1900-01-01 Online:2008-11-26 Published:2008-11-26
Contact: CHEN Guiyun

摘要/Abstract

摘要： 利用子群共轭类的性质, 结合Mousavi给出了非正规子群的共轭类类数为2的有限幂零群的分类, 得到了非正规子群的共轭类类数为2的有限群的完全分类, 校正了Mousavi给出的非正规子群的共轭类类数为２的有限非幂零群的分类.

关键词: 非正规子群, Dedekind群, 幂零群, 共轭类, 类数

Abstract: On the basis of the properties of conjugacy classes of nonnormal subgroups and the classification of finite nilpotent groups having exactly two conjugacy classes of nonnormal subgroups given by Mousavi, finite g roups having exactly two conjugacy classes of nonnormal subgroups are completely classified, revising the classification of finite nonnilpotent groups having exactly two conjugacy classes of nonnormal subgroups given by Mousavi.

Key words: nonnormal subgroups, Dedekind groups, nilpotent groups, conjugacy classes, class number

中图分类号:

O152.1

陈顺民,, 陈贵云. 非正规子群共轭类类数为2的有限群的一个注记[J]. J4, 2008, 46(06): 1097-1100.

CHEN Shunmin,, CHEN Guiyun. A Note on Finite Groups Having Exactly Two Conjugacy Classesof Nonnormal Subgroups[J]. J4, 2008, 46(06): 1097-1100.