TITLE:
Solving the Class Equation xd = β in an Alternating Group for Each β ∈ Cα ∩ Hnc and n > 1
AUTHORS:
Shuker Mahmood, Andrew Rajah
KEYWORDS:
Alternating Groups; Permutations; Conjugate Classes; Cycle Type; Frobenius Equation
JOURNAL NAME:
Advances in Linear Algebra & Matrix Theory,
Vol.2 No.2,
June
29,
2012
ABSTRACT: The main purpose of this paper is to solve the class equation in an alternating group, (i.e. find the solutions set ) and find the number of these solutions where ranges over the conjugacy class in and d is a positive integer. In this paper we solve the class equation in where , for all . is the complement set of where { of , with all parts of are different and odd}. is conjugacy class of and form class depends on the cycle type of its elements If and , then splits into the two classes of .