Solutions Of The Frobenius Class Equation In Alternating Groups - Kholil, Shuker Mahmood (2012)
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 .