Profinite completions of free-by-free groups contain everything

2023/12/11 by Bridson, Martin R. · 1 citation
#20E18 (20F65 #20E26 #20J06) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2312.06539

Abstract

Given an arbitrary, finitely presented, residually finite group Γ, one can construct a finitely generated, residually finite, free-by-free group M_Γ= F_∞\rtimes F₄ and an embedding M_Γ\hookrightarrow (F₄∗ Γ)× F₄ that induces an isomorphism of profinite completions. In particular, there is a free-by-free group whose profinite completion contains \widehatΓ as a retract.

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• Profinite properties of Coxeter groups

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