On a Family of Presentations Generalising Coxeter’s (l,m|n,k)Tools Bennett, E. P. (2021) On a Family of Presentations Generalising Coxeter’s (l,m|n,k). PhD thesis, University of Nottingham.
AbstractWe 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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