湘潭大学自然科学学报
湘潭大學自然科學學報
상담대학자연과학학보
NATURAL SCIENCE JOURNAL OF XIANGTAN UNIVERSITY
2008年
3期
12-20
,共9页
广义对称群%广义交错群%织积%共轭类
廣義對稱群%廣義交錯群%織積%共軛類
엄의대칭군%엄의교착군%직적%공액류
Generalized symmetric group%Generalized alternate group%Wreath product%Conjugacy class
该文首先推广Solomon引入的容许集的概念,然后利用容许集定义一类广义对称群ψ(l,m),该群是对称群S1与对称群Sm的织积.该文的目的是研究群ψ(l.m)的共轭类,计算共轭类的个数以及每个共轭类的阶.此外,还定义广义交错群 (l,m),并确定广义对称群ψ(l,m)的 (l,m)-共轭类.
該文首先推廣Solomon引入的容許集的概唸,然後利用容許集定義一類廣義對稱群ψ(l,m),該群是對稱群S1與對稱群Sm的織積.該文的目的是研究群ψ(l.m)的共軛類,計算共軛類的箇數以及每箇共軛類的階.此外,還定義廣義交錯群 (l,m),併確定廣義對稱群ψ(l,m)的 (l,m)-共軛類.
해문수선추엄Solomon인입적용허집적개념,연후이용용허집정의일류엄의대칭군ψ(l,m),해군시대칭군S1여대칭군Sm적직적.해문적목적시연구군ψ(l.m)적공액류,계산공액류적개수이급매개공액류적계.차외,환정의엄의교착군 (l,m),병학정엄의대칭군ψ(l,m)적 (l,m)-공액류.
In this paper we first generalize the concept of the admissible subset introduced by Solomon,and then using admissible subsets, we define a class of generalized symmetry groups ψ (l, m)which are the wreath product of the symmetric group S1 by the symmetric group Sm. The aim of this paper is to determine conjugacy classes of ψ (l, m), to compute the number of conjugacy classes and the order of a conjugaey class. Besides, we define generalized alternate groups (l,m) and determine (l,m) -conjugacy classes of the generalized symmetric group ψ (l, m) .
