Solutions Of The Frobenius Class Equation In Alternating Groups

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dc.contributor.authorKholil, Shuker Mahmood
dc.date.accessioned2019-06-27T01:05:24Z
dc.date.available2019-06-27T01:05:24Z
dc.date.issued2012
dc.description.abstractThe 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.en_US
dc.identifier.urihttp://hdl.handle.net/123456789/8411
dc.language.isoenen_US
dc.publisherUniversiti Sains Malaysiaen_US
dc.subjectSolutions of the frobenius classen_US
dc.subjectequation in alternating groupsen_US
dc.titleSolutions Of The Frobenius Class Equation In Alternating Groupsen_US
dc.typeThesisen_US
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