非正规子群共轭类类数为2的有限群的一个注记

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

Abstract

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

CLC Number:

O152.1

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.

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

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