Binary subgroups of direct products
We explore an elementary construction that produces finitely presented groups with diverse homological finiteness properties – the binary subgroups, B(Σ, µ) < G1 ×· · ·×Gm. These full subdirect products require strikingly few generators. If each Gi is finitely presented, B(Σ, µ) is finitely prese...
| Prif Awdur: | |
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| Fformat: | Journal article |
| Iaith: | English |
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EMS Press
2023
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| _version_ | 1826310340317544448 |
|---|---|
| author | Bridson, M |
| author_facet | Bridson, M |
| author_sort | Bridson, M |
| collection | OXFORD |
| description | We explore an elementary construction that produces finitely presented groups
with diverse homological finiteness properties – the binary subgroups, B(Σ, µ) < G1 ×· · ·×Gm.
These full subdirect products require strikingly few generators. If each Gi
is finitely presented,
B(Σ, µ) is finitely presented. When the Gi are non-abelian limit groups (e.g. free or surface
groups), the B(Σ, µ) provide new examples of finitely presented, residually-free groups that do
not have finite classifying spaces and are not of Stallings-Bieri type. These examples settle a
question of Minasyan relating different notions of rank for residually-free groups. Using binary
subgroups, we prove that if G1, . . . , Gm are perfect groups, each requiring at most r generators,
then G1 × · · · × Gm requires at most rblog2 m + 1c generators. |
| first_indexed | 2024-03-07T07:50:29Z |
| format | Journal article |
| id | oxford-uuid:c07c961b-ef24-45c5-a0b1-34dafab6ee6b |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:50:29Z |
| publishDate | 2023 |
| publisher | EMS Press |
| record_format | dspace |
| spelling | oxford-uuid:c07c961b-ef24-45c5-a0b1-34dafab6ee6b2023-07-05T09:22:42ZBinary subgroups of direct productsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c07c961b-ef24-45c5-a0b1-34dafab6ee6bEnglishSymplectic ElementsEMS Press2023Bridson, MWe explore an elementary construction that produces finitely presented groups with diverse homological finiteness properties – the binary subgroups, B(Σ, µ) < G1 ×· · ·×Gm. These full subdirect products require strikingly few generators. If each Gi is finitely presented, B(Σ, µ) is finitely presented. When the Gi are non-abelian limit groups (e.g. free or surface groups), the B(Σ, µ) provide new examples of finitely presented, residually-free groups that do not have finite classifying spaces and are not of Stallings-Bieri type. These examples settle a question of Minasyan relating different notions of rank for residually-free groups. Using binary subgroups, we prove that if G1, . . . , Gm are perfect groups, each requiring at most r generators, then G1 × · · · × Gm requires at most rblog2 m + 1c generators. |
| spellingShingle | Bridson, M Binary subgroups of direct products |
| title | Binary subgroups of direct products |
| title_full | Binary subgroups of direct products |
| title_fullStr | Binary subgroups of direct products |
| title_full_unstemmed | Binary subgroups of direct products |
| title_short | Binary subgroups of direct products |
| title_sort | binary subgroups of direct products |
| work_keys_str_mv | AT bridsonm binarysubgroupsofdirectproducts |