Gerald Williams

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math.GR2025

All hyperbolic cyclically presented groups with positive length three relators

Ihechukwu Chinyere, Martin Edjvet, Gerald Williams

We consider the cyclically presented groups defined by cyclic presentations with $2 m$ generators $x_{i}$ whose relators are the $2 m$ positive length three relators $x_ix_{i+1}x_{i+m-…

math.GR2024

Smith forms of matrices in Companion Rings, with group theoretic and topological applications

Vanni Noferini, Gerald Williams

Let $R$ be a commutative ring and $g (t) \in R [t]$ a monic polynomial. The commutative ring of polynomials $f (C_{g})$ in the companion matrix $C_{g}$ of $g (t)$ , where $f (t) \in R [t]$ , is…