Free-by-cyclic groups are not relatively profinitely rigid

2026/07/26 by Carl-Fredrik Nyberg-Brodda
#math.GR

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Abstract

For m=5 and for every m ≥ 7 we construct families of pairwise non-isomorphic free-by-cyclic groups isomorphic to F_2m \rtimes ℤ having isomorphic profinite completions. This answers a question of Bridson & Reid from 2015.

Citations

• Embedding finitely generated free-by-cyclic groups in finitely generated free-by-cyclic groups
• A hyperbolic free-by-cyclic group determined by its finite quotients
• Profinite rigidity, Kleinian groups, and the cofinite Hopf property
• Absolute profinite rigidity and hyperbolic geometry
• On finitely generated profinite groups I: strong completeness and uniform bounds

Related

• On profinite rigidity amongst free-by-cyclic groups I: the generic case
• Profinite rigidity for free-by-cyclic groups with centre
• Lack of profinite rigidity among extensions with free quotient
• Profinite completions of free-by-free groups contain everything
• A hyperbolic free-by-cyclic group determined by its finite quotients