引用本文:黄宇, 宋科研.用不可补子群个数刻画单群A5[J].西南大学学报(自然科学版),2018,40(12):90~93
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用不可补子群个数刻画单群A5
黄宇, 宋科研
西南大学 数学与统计学院, 重庆 400715
摘要:
G是有限群,HG.如果G中存在子群KG,满足G=KH,且HK=1,那么称HG中可补.研究子群的可补性对有限群结构和性质的影响是群论研究中十分重要的课题.给出了5次交错群A5的一个新刻画,即60阶群GA5的充分必要条件是G中只有46个不可补子群.
关键词:  不可补子群  5次交错群  Sylow子群
DOI:10.13718/j.cnki.xdzk.2018.12.014
分类号:O152.1
基金项目:国家自然科学基金项目(11501465).
Characterizing the Simple Group A5 by the Number of Uncomplemented Subgroups
HUANG Yu, SONG Ke-yan
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
Abstract:
Let G be a finite group, HG. If there exists a subgroup K of G such that G=HK and HK=1, then H is called complemented in G. The subgroup's complementarity on the structure and properties of finite groups is a very important topic in group theory. A new characterization of the alternating group A5 is given, i.e., let G be a group of order 60, GA5 if and only if G only has 46 uncomplemented subgroups.
Key words:  uncomplemented subgroup  alternating group of degree 5  Sylow subgroup
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