Solving the Class Equation x^d = β in an Alternating Group for Each β ∈ C^α ∩ H_n^c and n > 1

Shuker Mahmood, Andrew Rajah

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

DOI: 10.4236/alamt.2012.22002                

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 .

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

References

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