Author(s)

Shuker Mahmood, Andrew Rajah

Department of Mathematics, College of Science, University of Basra, Basra, Iraq.
School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia.

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 .

Alternating Groups; Permutations; Conjugate Classes; Cycle Type; Frobenius Equation

Mahmood, S. and Rajah, A. (2012) Solving the Class Equation x^d = β in an Alternating Group for Each β ∈ C^α ∩ H_n^c and n > 1. Advances in Linear Algebra & Matrix Theory, 2, 13-19. doi: 10.4236/alamt.2012.22002.