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Solving the Class Equation xd = β in an Alternating Group for Each β ∈ Cα ∩ Hnc and n > 1

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DOI: 10.4236/alamt.2012.22002    3,338 Downloads   10,538 Views   Citations

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 .

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

S. Mahmood and A. Rajah, "Solving the Class Equation xd = β in an Alternating Group for Each β ∈ Cα ∩ Hnc and n > 1," Advances in Linear Algebra & Matrix Theory, Vol. 2 No. 2, 2012, pp. 13-19. doi: 10.4236/alamt.2012.22002.

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