摘要
利用内外-∑群和极小非-∑群的性质构造极小反例对有限群进行研究是研究有限群的重要方法。而群的特征标较好地反映了群的数量性质,在群论、物理学、化学以及小波理论研究中也非常重要。综合应用极小反例和群特征标对有限群进行研究是一种新的研究思路。在1N-群性质推广、极小非1A-的完全分类以及亚循环群非线性特征标性质研究的基础上,用极小反例的方法对kNP-群的性质作了进一步的研究;着眼于其特征标,构造出一类M-群。
Constructing a minimal counterexample by virtue of properties of inner ∑ groups, outer ∑ groups and minimal non ∑ groups is an important method for studying finite groups. On the other hand, the characters of groups which embody numerical properties of finite groups are applied extensively to theory of finite groups, physics, chemistry and theory of wavelet. Combining mini counterexamples with characters of finite groups to study finite groups is a new technique. Based upon the extension to the properties of 1 N groups, the complete classification of minimal non 1 A groups and the nonlinear irreducible characters of meta cyclic groups, some novel properties of kN P groups are given, and a class of M groups are constructed with a view of characters of groups.
出处
《重庆大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2005年第4期110-112,共3页
Journal of Chongqing University
基金
博士后科学基金资助项目(2004035521)
重庆市自然科学基金资助项目(8651)
关键词
kN-群
内外-∑群
特征标
M-群
kN group
inner ∑group and outer ∑ group
character
M-group
