Free-by-cyclic groups are not relatively profinitely rigid

Abstract

For $m=5$ and for every $m\ge 7$ we construct families of pairwise non-isomorphic free-by-cyclic groups isomorphic to $F_{2m}⋊\mathbb{Z}$ having isomorphic profinite completions. This answers a question of Bridson & Reid from 2015.

10 pages. Comments welcome!