Profinite completions of free-by-free groups contain everything
Given an arbitrary, finitely presented, residually finite group Γ, one can construct a finitely generated, residually finite, free-by-free group <em>M</em><sub>Γ</sub> = <em>F</em><sub>∞</sub> ⋊ <em>F</em><sub>4</sub> and an emb...
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| Médium: | Journal article |
| Jazyk: | English |
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Oxford University Press
2024
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| Shrnutí: | Given an arbitrary, finitely presented, residually finite group Γ, one can construct a finitely generated, residually finite, free-by-free group <em>M</em><sub>Γ</sub> = <em>F</em><sub>∞</sub> ⋊ <em>F</em><sub>4</sub> and an embedding <em>M</em><sub>Γ</sub> ↪ (<em>F</em><sub>4</sub> ∗ Γ) × <em>F</em><sub>4</sub> that induces an isomorphism of profinite completions. In particular, there is a free-by-free group whose profinite completion contains Γ as a retract.
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