摘要
设G是有限群,并设Con(G)是由G的一切共轭类组成的集合。本文目的是考察Con(G)的算术结构对G的群结构的影响。我们着重于Con(G)的p-部分结构,并得到关于p-幂零群的两个定理。这里,p表示一个有限群的阶的最小素因子,用这两个定理,我们还得到若干结果,其中两个改进了D.Chillag和M.Herzog关于共轭类长的两个结果.
Let G be a finite group, and let Con(G) be the set of all the con-jugacy classes of G. The purpose of this paper is to investigate the influence of the arithmetical structure of Con(G) on the group structure of G. We put our emphasis on the p-part structure of Con(G),and obtain two theorem:on p-nilpotent groups.Here,p denotes the least prime divisor of order of a finite group.Using the two theorems, we also get several results,two of which improve the two results of D. Chillag and M. Herzog on the length of conjugacy classes.
出处
《数学进展》
CSCD
北大核心
1994年第5期405-410,共6页
Advances in Mathematics(China)
关键词
共轭类
超可解
有限群
P幂零
length of conjugacy classes
p-nilpotent
supersolvable
p-part
Sylow tower