Kholil, Shuker Mahmood
(2012)
Solutions Of The Frobenius Class Equation In Alternating Groups.
PhD thesis, Universiti Sains Malaysia.
Abstract
The Frobenius equation d x in finite groups was introduced by G. Frobenius and studied by many others who dealt with several types of finite groups, including finite cyclic groups, m generated finite groups, finite p groups, and wreath products of finite groups. In the current study, the number of solutions for the class equation x A( ) d in an alternating group n A is found and it is observed that ranges over A( ) the conjugacy class of in n A . In this thesis, four cases of solutions to the class equation d x in n A are discussed. Firstly, the class equation d x in n A , where H C c n , for all n 1 is solved and the number of solutions of the above equation with n H { C of n S | n 1, with all parts k of different and odd} is found, where C is a conjugacy class of n S .
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