摘要
MT(G)=(m_1,m_2,…,m_k)称为G的极大子群共轭类型,其中m_1≤m_2≤…≤m_k,表示G有k个极大子群共轭类,并且第i个共轭类类长为m_i.利用极大子群共轭类型给出全部交错群和部分对称群的一个新刻画.
MT(G) = (m1, m2,…… , mk) is called the type of conjugacy classes of maximal subgroups of finite group G, where m1≤ m2≤… ≤ mk, which implies that G has exactly k classes of conjugate maximal subgroups, and the class length of the i-th conjugacy class is mi. This paper gives a new characterization of all alternating groups and some symmetric groups by the type of conjugacy classes of maximal subgroups.
出处
《数学年刊(A辑)》
CSCD
北大核心
2009年第2期281-290,共10页
Chinese Annals of Mathematics
基金
国家自然科学基金(No.10871021
No.10871032)
"Agencija za raziskovalno dejavnost Republike Slovenije"
proj.mladi raziskovalci
"Agencija za raziskovalno dejevnost Republike Slovenije".research program P1-0285
高等学校博士学科点专项科研基金(No.20060285002)资助的项目.
关键词
极大子群
共轭类型
单群
交错群
对称群
Maximal subgroup, The type of conjugacy classes, Simple group Alternating group, Symmetric group