Solutions Of The Frobenius Class Equation In Alternating Groups
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Date
2012
Authors
Kholil, Shuker Mahmood
Journal Title
Journal ISSN
Volume Title
Publisher
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 . Next, the class equation d x in n A where H C n
and n {1,2,5,6,10,14} is solved and the number of solutions is determined.
Thirdly, the class equation x A e d (1) in n A is solved and the number of
solutions of this equation where A(1) is the identity conjugacy class in n A is
determined. Finally, the class equation d x in n A , where H C n and
n is solved and the number of its solutions is found.
Description
Keywords
Solutions of the frobenius class , equation in alternating groups