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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| Format: | Journal article |
| Język: | English |
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Oxford University Press
2024
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| _version_ | 1826314480729980928 |
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| author | Bridson, MR |
| author_facet | Bridson, MR |
| author_sort | Bridson, MR |
| collection | OXFORD |
| description | 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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| first_indexed | 2024-03-07T08:13:50Z |
| format | Journal article |
| id | oxford-uuid:3a927b07-2812-4e3c-b2de-33d6d03e5138 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:33:09Z |
| publishDate | 2024 |
| publisher | Oxford University Press |
| record_format | dspace |
| spelling | oxford-uuid:3a927b07-2812-4e3c-b2de-33d6d03e51382024-09-11T12:27:04ZProfinite completions of free-by-free groups contain everythingJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3a927b07-2812-4e3c-b2de-33d6d03e5138EnglishSymplectic ElementsOxford University Press2024Bridson, MRGiven 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. |
| spellingShingle | Bridson, MR Profinite completions of free-by-free groups contain everything |
| title | Profinite completions of free-by-free groups contain everything |
| title_full | Profinite completions of free-by-free groups contain everything |
| title_fullStr | Profinite completions of free-by-free groups contain everything |
| title_full_unstemmed | Profinite completions of free-by-free groups contain everything |
| title_short | Profinite completions of free-by-free groups contain everything |
| title_sort | profinite completions of free by free groups contain everything |
| work_keys_str_mv | AT bridsonmr profinitecompletionsoffreebyfreegroupscontaineverything |