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

DOI: 10.4236/alamt.2012.22002   PDF   HTML   XML   3,504 Downloads   10,761 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 .

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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.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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