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...

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Main Author: Dennis, Mark
Format: Thesis (University of Nottingham only)
Language:English
Published: 2017
Online Access:https://eprints.nottingham.ac.uk/41835/
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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)
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institution University of Nottingham Malaysia Campus
institution_category Local University
language English
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publishDate 2017
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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/