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/ |
| Summary: | 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. |
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