On a Family of Presentations Generalising Coxeter’s (l,m|n,k)
We study the groups with presentation (l,m|n,k|p,q) := <a,b|a^l ,b^m ,(ab)^n ,(a^p b^q )^k>, in an attempt to characterise which parameter-sets give rise to a finite group, using a combination of geometric and computational methods, along with more elementary presentation manipulation techniqu...
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
| Published: |
2021
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| Online Access: | https://eprints.nottingham.ac.uk/64841/ |
| _version_ | 1848800173345472512 |
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| author | Bennett, E. P. |
| author_facet | Bennett, E. P. |
| author_sort | Bennett, E. P. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We study the groups with presentation (l,m|n,k|p,q) := <a,b|a^l ,b^m ,(ab)^n ,(a^p b^q )^k>, in an attempt to characterise which parameter-sets give rise to a finite group, using a combination of geometric and computational methods, along with more elementary presentation manipulation techniques. We achieve a full characterisation for the case l = 2p,m = 2q, and a characterisation with a few families of exceptions under the simplifying assumption 1/n + 1/k ≤ 1/2. |
| first_indexed | 2025-11-14T20:47:21Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-64841 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:47:21Z |
| publishDate | 2021 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-648412021-08-04T04:41:05Z https://eprints.nottingham.ac.uk/64841/ On a Family of Presentations Generalising Coxeter’s (l,m|n,k) Bennett, E. P. We study the groups with presentation (l,m|n,k|p,q) := <a,b|a^l ,b^m ,(ab)^n ,(a^p b^q )^k>, in an attempt to characterise which parameter-sets give rise to a finite group, using a combination of geometric and computational methods, along with more elementary presentation manipulation techniques. We achieve a full characterisation for the case l = 2p,m = 2q, and a characterisation with a few families of exceptions under the simplifying assumption 1/n + 1/k ≤ 1/2. 2021-08-04 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en cc_by https://eprints.nottingham.ac.uk/64841/1/coxeter.pdf Bennett, E. P. (2021) On a Family of Presentations Generalising Coxeter’s (l,m|n,k). PhD thesis, University of Nottingham. Combinatorial group theory finitely presented groups finiteness computational algebra |
| spellingShingle | Combinatorial group theory finitely presented groups finiteness computational algebra Bennett, E. P. On a Family of Presentations Generalising Coxeter’s (l,m|n,k) |
| title | On a Family of Presentations Generalising Coxeter’s (l,m|n,k) |
| title_full | On a Family of Presentations Generalising Coxeter’s (l,m|n,k) |
| title_fullStr | On a Family of Presentations Generalising Coxeter’s (l,m|n,k) |
| title_full_unstemmed | On a Family of Presentations Generalising Coxeter’s (l,m|n,k) |
| title_short | On a Family of Presentations Generalising Coxeter’s (l,m|n,k) |
| title_sort | on a family of presentations generalising coxeter’s (l,m|n,k) |
| topic | Combinatorial group theory finitely presented groups finiteness computational algebra |
| url | https://eprints.nottingham.ac.uk/64841/ |