几乎散在单群的一种刻画

数学物理学报 ›› 2014, Vol. 34 ›› Issue (6): 1456-1464.

几乎散在单群的一种刻画

陈彦恒^1,2|陈贵云^1*

1.西南大学数学与统计学院重庆 400715;
2.重庆三峡学院数学与统计学院重庆 404100

收稿日期:2013-03-29 修回日期:2014-04-12 出版日期:2014-12-25 发布日期:2014-12-25
通讯作者: 陈贵云,gychen@swu.edu.cn E-mail:math_yan@126.com; gychen@swu.edu.cn
基金资助:
国家自然科学基金(11271301)、重庆市科委自然科学基金计划资助项目(CSTC2014jcyjA00009)、重庆市教委科学技术研究项目(KJ1401006)和中央高校基本科研业务费专项资金资助

A Characterization of Almost Sporadic Simple Groups

CHEN Yan-Heng^1,2, CHEN Gui-Yun^1*

1.School of Mathematics and Statistics, Southwest University, Chongqing 400715;
2.School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 400410

Received:2013-03-29 Revised:2014-04-12 Online:2014-12-25 Published:2014-12-25
Contact: CHEN Gui-Yun,gychen@swu.edu.cn E-mail:math_yan@126.com; gychen@swu.edu.cn
Supported by:
国家自然科学基金(11271301)、重庆市科委自然科学基金计划资助项目(CSTC2014jcyjA00009)、重庆市教委科学技术研究项目(KJ1401006)和中央高校基本科研业务费专项资金资助

摘要/Abstract

摘要：

设L是一个有限非交换单群. 若有限群G 满足: L≤G≤Aut(L) , 则称G 是相关于L 的几乎单群. 特别地, 若L 是一个散在单群, 则称G 是相关于L 的几乎散在单群. 该文证明了所有几乎散在单群可被其阶和不多于两个特殊共轭类长唯一确定.

关键词: 有限群, 几乎散在单群, 素图, 共轭类长

Abstract:

A finite group G is said to be an almost simple related to L if and only if L≤G≤Aut(L) for some simple group L. Further, if L is a sporadic simple group, then say that G is an almost sporadic simple group related to L. In this paper, we prove that all almost sporadic simple groups can be determined uniquely by their orders and no more than two special conjugacy class lengths.

Key words: Finite group, Almost sporadic simple groups, Prime graph, Conjugacy class length

中图分类号:

20D05

陈彦恒, 陈贵云. 几乎散在单群的一种刻画[J]. 数学物理学报, 2014, 34(6): 1456-1464.

CHEN Yan-Heng, CHEN Gui-Yun. A Characterization of Almost Sporadic Simple Groups[J]. Acta mathematica scientia,Series A, 2014, 34(6): 1456-1464.

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