Weak commutativity and finiteness properties of groups
We consider the groupX(G) obtained fromG∗Gby forcing each elementgin the first freefactor to commute with the copy ofgin the second free factor. Deceptively complicated finitelypresented groups arise from this construction:X(G) is finitely presented if and only ifGis finitelypresented, but ifFis a n...
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| Formato: | Journal article |
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London Mathematical Society
2018
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| _version_ | 1826291714991587328 |
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| author | Bridson, M Kochloukova, D |
| author_facet | Bridson, M Kochloukova, D |
| author_sort | Bridson, M |
| collection | OXFORD |
| description | We consider the groupX(G) obtained fromG∗Gby forcing each elementgin the first freefactor to commute with the copy ofgin the second free factor. Deceptively complicated finitelypresented groups arise from this construction:X(G) is finitely presented if and only ifGis finitelypresented, but ifFis a non-abelian free group of finite rank thenX(F) has a subgroup of finiteindex whose third homology is not finitely generated. |
| first_indexed | 2024-03-07T03:03:34Z |
| format | Journal article |
| id | oxford-uuid:b1c329db-bc80-44ac-b14d-69f48e91f75b |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:03:34Z |
| publishDate | 2018 |
| publisher | London Mathematical Society |
| record_format | dspace |
| spelling | oxford-uuid:b1c329db-bc80-44ac-b14d-69f48e91f75b2022-03-27T04:06:33ZWeak commutativity and finiteness properties of groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:b1c329db-bc80-44ac-b14d-69f48e91f75bSymplectic Elements at OxfordLondon Mathematical Society2018Bridson, MKochloukova, DWe consider the groupX(G) obtained fromG∗Gby forcing each elementgin the first freefactor to commute with the copy ofgin the second free factor. Deceptively complicated finitelypresented groups arise from this construction:X(G) is finitely presented if and only ifGis finitelypresented, but ifFis a non-abelian free group of finite rank thenX(F) has a subgroup of finiteindex whose third homology is not finitely generated. |
| spellingShingle | Bridson, M Kochloukova, D Weak commutativity and finiteness properties of groups |
| title | Weak commutativity and finiteness properties of groups |
| title_full | Weak commutativity and finiteness properties of groups |
| title_fullStr | Weak commutativity and finiteness properties of groups |
| title_full_unstemmed | Weak commutativity and finiteness properties of groups |
| title_short | Weak commutativity and finiteness properties of groups |
| title_sort | weak commutativity and finiteness properties of groups |
| work_keys_str_mv | AT bridsonm weakcommutativityandfinitenesspropertiesofgroups AT kochloukovad weakcommutativityandfinitenesspropertiesofgroups |