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Conjugacy Classes of a Class of Generalized Symmetric Groups

Author: NiLei
Tutor: CaoYouAn
School: Xiangtan University
Course: Basic mathematics
Keywords: Generalized symmetric group Generalized alternating group Divide Conjugacy classes
CLC: O152.1
Type: Master's thesis
Year: 2008
Downloads: 16
Quote: 0
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Abstract


Let (l, m) is an ordered pair of positive integers . ORDER l = { 1,2 , ... , l }, m = {1,2 , ... , m } , and s = l x m = {(1,1), ..., (l, 1), (1,2), ..., (l, 2), ..., (1, m), ..., (l, m)}. S_m ~ l indicates the symmetry group of the set s s a subset of I called allowable, if ( i, j ) ∈ I , then for any i '∈ L \\ I ( i' , j ) (?) I. set ( ? ) ( l, m ) is by S_M ~~ L s allowable sub- set maps to allow a subset of those replacement subgroups constituted , it is called type ( l, m ) generalized symmetry group . generalized symmetry group (?) (l, m) even replacement constitute a subgroup called Generalized alternating groups , denoted by ( ? ) ( l , m ) the purpose of this paper is to study the generalized symmetry group ( ?) (l, m) conjugacy classes , mainly the following : ( 1 ) to determine the ( ? ) ( l , m ) of two replacement necessary and sufficient condition for the conjugate ; ( 2 ) to determine the ( ? ) (l m) of the number of conjugate classes ; (3) determining ( ? ) ( l, m ) of a conjugated class containing a number of permutation ; (4 ) determining (?) (l, m) of the two replacement ( ? ) conjugate ( l , m ) necessary and sufficient conditions .

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Group theory > Finite group theory
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