一类广义对称群的共轭类

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.

Conjugacy Classes of A Class of Generalized Symmetric Groups

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) .