Solutions Of The Frobenius Class Equation In Alternating Groups
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...
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2012
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my-usm-ep.448902019-07-05T08:02:37Z Solutions Of The Frobenius Class Equation In Alternating Groups 2012 Kholil, Shuker Mahmood QA1-939 Mathematics 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 . 2012 Thesis http://eprints.usm.my/44890/ http://eprints.usm.my/44890/1/SHUKER%20MAHMOOD%20KHOLIL.pdf application/pdf en public phd doctoral Universiti Sains Malaysia Pusat Pengajian Sains Matematik |
| institution |
Universiti Sains Malaysia |
| collection |
USM Institutional Repository |
| language |
English |
| topic |
QA1-939 Mathematics |
| spellingShingle |
QA1-939 Mathematics Kholil, Shuker Mahmood Solutions Of The Frobenius Class Equation In Alternating Groups |
| description |
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 . |
| format |
Thesis |
| qualification_name |
Doctor of Philosophy (PhD.) |
| qualification_level |
Doctorate |
| author |
Kholil, Shuker Mahmood |
| author_facet |
Kholil, Shuker Mahmood |
| author_sort |
Kholil, Shuker Mahmood |
| title |
Solutions Of The Frobenius Class Equation In Alternating Groups |
| title_short |
Solutions Of The Frobenius Class Equation In Alternating Groups |
| title_full |
Solutions Of The Frobenius Class Equation In Alternating Groups |
| title_fullStr |
Solutions Of The Frobenius Class Equation In Alternating Groups |
| title_full_unstemmed |
Solutions Of The Frobenius Class Equation In Alternating Groups |
| title_sort |
solutions of the frobenius class equation in alternating groups |
| granting_institution |
Universiti Sains Malaysia |
| granting_department |
Pusat Pengajian Sains Matematik |
| publishDate |
2012 |
| url |
http://eprints.usm.my/44890/1/SHUKER%20MAHMOOD%20KHOLIL.pdf |
| _version_ |
1747821420703907840 |