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...
Main Author: | |
---|---|
Format: | Journal article |
Language: | English |
Published: |
2007
|
_version_ | 1797063336042430464 |
---|---|
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 |