Detecting large groups
Let G be a finitely presented group, and let p be a prime. Then G is 'large' (respectively, 'p-large') if some normal subgroup with finite index (respectively, index a power of p) admits a non-abelian free quotient. This paper provides a variety of new methods for detecting wheth...
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| Format: | Journal article |
| Language: | English |
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2007
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| _version_ | 1797063336042430464 |
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| author | Lackenby, M |
| author_facet | Lackenby, M |
| author_sort | Lackenby, M |
| collection | OXFORD |
| description | Let G be a finitely presented group, and let p be a prime. Then G is 'large' (respectively, 'p-large') if some normal subgroup with finite index (respectively, index a power of p) admits a non-abelian free quotient. This paper provides a variety of new methods for detecting whether G is large or p-large. These relate to the group's profinite and pro-p completions, to its first L2-Betti number and to the existence of certain finite index subgroups with 'rapid descent'. The paper draws on new topological and geometric techniques, together with a result on error-correcting codes. |
| first_indexed | 2024-03-06T20:58:22Z |
| format | Journal article |
| id | oxford-uuid:3a083e31-1011-40ed-a53d-e9f1af8590f1 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:58:22Z |
| publishDate | 2007 |
| record_format | dspace |
| spelling | oxford-uuid:3a083e31-1011-40ed-a53d-e9f1af8590f12022-03-26T13:59:07ZDetecting large groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3a083e31-1011-40ed-a53d-e9f1af8590f1EnglishSymplectic Elements at Oxford2007Lackenby, MLet G be a finitely presented group, and let p be a prime. Then G is 'large' (respectively, 'p-large') if some normal subgroup with finite index (respectively, index a power of p) admits a non-abelian free quotient. This paper provides a variety of new methods for detecting whether G is large or p-large. These relate to the group's profinite and pro-p completions, to its first L2-Betti number and to the existence of certain finite index subgroups with 'rapid descent'. The paper draws on new topological and geometric techniques, together with a result on error-correcting codes. |
| spellingShingle | Lackenby, M Detecting large groups |
| title | Detecting large groups |
| title_full | Detecting large groups |
| title_fullStr | Detecting large groups |
| title_full_unstemmed | Detecting large groups |
| title_short | Detecting large groups |
| title_sort | detecting large groups |
| work_keys_str_mv | AT lackenbym detectinglargegroups |