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arXiv · 2607.23780

Free-by-cyclic groups are not relatively profinitely rigid

Carl-Fredrik Nyberg-Brodda
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Abstract

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

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Carl-Fredrik Nyberg-Brodda. 2026-07-26. Free-by-cyclic groups are not relatively profinitely rigid. https://arxiv.org/abs/2607.23780

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