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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| Format: | Thesis |
| Language: | English |
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2012
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| Online Access: | http://eprints.usm.my/44890/1/SHUKER%20MAHMOOD%20KHOLIL.pdf |
| _version_ | 1825835053075136512 |
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| author | Kholil, Shuker Mahmood |
| author_facet | Kholil, Shuker Mahmood |
| author_sort | Kholil, Shuker Mahmood |
| collection | USM |
| 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 . |
| first_indexed | 2024-03-06T15:31:56Z |
| format | Thesis |
| id | usm.eprints-44890 |
| institution | Universiti Sains Malaysia |
| language | English |
| last_indexed | 2024-03-06T15:31:56Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | usm.eprints-448902019-07-05T08:02:37Z http://eprints.usm.my/44890/ Solutions Of The Frobenius Class Equation In Alternating Groups 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 NonPeerReviewed application/pdf en http://eprints.usm.my/44890/1/SHUKER%20MAHMOOD%20KHOLIL.pdf Kholil, Shuker Mahmood (2012) Solutions Of The Frobenius Class Equation In Alternating Groups. PhD thesis, Universiti Sains Malaysia. |
| spellingShingle | QA1-939 Mathematics Kholil, Shuker Mahmood Solutions Of The Frobenius Class Equation In Alternating Groups |
| title | 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_short | Solutions Of The Frobenius Class Equation In Alternating Groups |
| title_sort | solutions of the frobenius class equation in alternating groups |
| topic | QA1-939 Mathematics |
| url | http://eprints.usm.my/44890/1/SHUKER%20MAHMOOD%20KHOLIL.pdf |
| work_keys_str_mv | AT kholilshukermahmood solutionsofthefrobeniusclassequationinalternatinggroups |