Alan W. Reid

activity

20232026

collaborators

4 papers

math.GR2026

Subgroups with all finite lifts isomorphic are conjugate

Ido Karshon, Alexander Lubotzky, D. B. McReynolds +2

We show that for non-conjugate subgroups $G_{1}$ and $G_{2}$ of a finite group $G$ there exists an extension of $G$ (by a finite group) in which the pre-images of $G_{1}$ and $G_{2}$ are n…

math.GR2025

Relatively hyperbolic groups, Grothendieck pairs, and uncountable profinite ambiguity among fibre products

Martin R. Bridson, Alan W. Reid

These notes expand upon our lectures on {\em profinite rigidity} at the international colloquium on randomness, geometry and dynamics, organised by TIFR Mumbai at IISER Pune in Jan…

math.GR2023

Absolute profinite rigidity, direct products, and finite presentability

M. R. Bridson, A. W. Reid, R. Spitler

We prove that there exist finitely presented, residually finite groups that are profinitely rigid in the class of all finitely presented groups but not in the class of all finitely…

math.GT2023

Determining knot groups by finite quotients

Tamunonye Cheetham-West, Alan W. Reid

We prove that hyperbolic 2-bridge knots are determined amongst all compact 3-manifolds by the profinite completions of their knot groups.