M. Bridson

collaborators

15 papers

math.GR2026

Conjugator length in finitely presented groups

Martin R. Bridson, Timothy R. Riley, Andrew W. Sale

The conjugator length function of a finitely generated group $G$ gives the minimal upper bound on the length of a conjugator for a pair of words that represent conjugate elements i…

math.GR2026

Conjugacy in fibre products, distortion, and the geometry of cyclic subgroups

Martin R Bridson

We investigate the complexity of the conjugacy problem for fibre products in torsion-free hyperbolic groups. Let $G$ be a torsion-free hyperbolic group and let $P < G \times G$ be the…

math.GR2026

On the conjugacy problem for subdirect products of hyperbolic groups

Martin R. Bridson

If $G_{1}$ and $G_{2}$ are torsion-free hyperbolic groups and $P < G_{1} \times G_{2}$ is a finitely generated subdirect product, then the conjugacy problem in $P$ is solvable if and only if…

math.GR2026

Linear Diophantine equations and conjugator length in 2-step nilpotent groups

Martin R. Bridson, Timothy R. Riley

We establish upper bounds on the lengths of minimal conjugators in 2-step nilpotent groups. These bounds exploit the existence of small integral solutions to systems of linear Diop…

math.GR2026

The lengths of conjugators in the model filiform groups

Martin R. Bridson, Timothy R. Riley

The conjugator length function of a finitely generated group $I^$ gives the optimal upper bound on the length of a shortest conjugator for any pair of conjugate elements in the bal…

math.GR2025

Groups with fast-growing conjugator length functions

Martin R. Bridson, Timothy R. Riley

We construct the first examples of finitely presented groups whose conjugator length function is exponential; these are central extensions of groups of the form $F_{m} ⋊ F_{2}$ . F…