On a family of quotients of the von Dyck groups
In this publication, we investigate the groups H(m, n, p, q |k) defined by the presentation <x, y|x^m, y^n, (xy)^p, (xy^k)^q> and determine finiteness and infiniteness for these parameters as far as possible using geometric arguments, principally through pictures and curvature. We state and s...
| Main Author: | |
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
| Published: |
2017
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| Online Access: | https://eprints.nottingham.ac.uk/41835/ |
| _version_ | 1848796363963236352 |
|---|---|
| author | Dennis, Mark |
| author_facet | Dennis, Mark |
| author_sort | Dennis, Mark |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | In this publication, we investigate the groups H(m, n, p, q |k) defined by the presentation <x, y|x^m, y^n, (xy)^p, (xy^k)^q> and determine finiteness and infiniteness for these parameters as far as possible using geometric arguments, principally through pictures and curvature. We state and subsequently prove theorems relating to infiniteness, and also discuss troublesome cases where spherical pictures may arise. We also provide a list of known finite groups and unresolved cases in Appendix A. |
| first_indexed | 2025-11-14T19:46:48Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-41835 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T19:46:48Z |
| publishDate | 2017 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-418352025-02-28T13:44:02Z https://eprints.nottingham.ac.uk/41835/ On a family of quotients of the von Dyck groups Dennis, Mark In this publication, we investigate the groups H(m, n, p, q |k) defined by the presentation <x, y|x^m, y^n, (xy)^p, (xy^k)^q> and determine finiteness and infiniteness for these parameters as far as possible using geometric arguments, principally through pictures and curvature. We state and subsequently prove theorems relating to infiniteness, and also discuss troublesome cases where spherical pictures may arise. We also provide a list of known finite groups and unresolved cases in Appendix A. 2017-07-12 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en arr https://eprints.nottingham.ac.uk/41835/1/Corrected%20Final%20Thesis.pdf Dennis, Mark (2017) On a family of quotients of the von Dyck groups. PhD thesis, University of Nottingham. |
| spellingShingle | Dennis, Mark On a family of quotients of the von Dyck groups |
| title | On a family of quotients of the von Dyck groups |
| title_full | On a family of quotients of the von Dyck groups |
| title_fullStr | On a family of quotients of the von Dyck groups |
| title_full_unstemmed | On a family of quotients of the von Dyck groups |
| title_short | On a family of quotients of the von Dyck groups |
| title_sort | on a family of quotients of the von dyck groups |
| url | https://eprints.nottingham.ac.uk/41835/ |