引用本文:周茹, 吕恒.交错群A5的新刻画[J].西南师范大学学报(自然科学版),2019,44(12):6~9
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交错群A5的新刻画
周茹, 吕恒
西南大学 数学与统计学院, 重庆 400715
摘要:
利用在不同的共轭类上取值均不相同的特征标的个数刻画了A5.60阶群除了A5外均可解.主要通过对所有60阶可解群的结构以及它们的特征标的性质进行分析,得出在各个60阶可解群的特征标中,满足在不同的共轭类上取值均不相同这一条件的特征标的个数均不为2.最后分析了A5的特征标性质,得出只有A5是满足条件的60阶群.采用由特殊到一般以及一一排除的方法,证明了如果一个有限群G,其阶为60,并且满足在G的所有不可约特征标中,恰好存在两个不可约特征标,使得这两个特征标在不同的共轭类上均为不同的取值,则这个群一定同构于A5.
关键词:  有限群  特征标  共轭类
DOI:10.13718/j.cnki.xsxb.2019.12.002
分类号:O152.1
基金项目:国家自然科学基金项目(11471266).
A New Characterization of Alternating Group A5
ZHOU Ru, Lü Heng
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
Abstract:
The number has been used in this paper of irreducible characters whose values are differently in different conjugacy classes to characterrises A5. The 60-order finite groups is solvable except A5, so, by analyzing the structures and the nature of the characters of all the 60-order groups, finds that among all the solvable 60-order groups, the number of characters which satisfy the condition that their values differ in different conjugate classes is not two. Whereas unsolvable 60-order group A5 has two characters whose values are dissimilar in different conjugate classes. It is concluded that A5 is the only 60-order group that meets the condition. From special to general, the paper employs the elimination method proved that if a 60-order finite group has two irreducible characters which value differently in different conjugacy classes, it has to be A5.
Key words:  finite group  character  conjugacy class
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