Approximate subgroups of linear groups
We establish various results on the structure of approximate subgroups in linear groups such as SL_n(k) that were previously announced by the authors. For example, generalising a result of Helfgott (who handled the cases n = 2 and 3), we show that any approximate subgroup of SL_n(F_q) which generate...
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| Format: | Journal article |
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2010
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| _version_ | 1797061935229829120 |
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| author | Breuillard, E Green, B Tao, T |
| author_facet | Breuillard, E Green, B Tao, T |
| author_sort | Breuillard, E |
| collection | OXFORD |
| description | We establish various results on the structure of approximate subgroups in linear groups such as SL_n(k) that were previously announced by the authors. For example, generalising a result of Helfgott (who handled the cases n = 2 and 3), we show that any approximate subgroup of SL_n(F_q) which generates the group must be either very small or else nearly all of SL_n(F_q). The argument generalises to other absolutely almost simple connected (and non-commutative) algebraic groups G over a finite field k. In a subsequent paper, we will give applications of this result to the expansion properties of Cayley graphs. |
| first_indexed | 2024-03-06T20:38:18Z |
| format | Journal article |
| id | oxford-uuid:3360a503-d419-4508-8f4e-13b15d26b8e1 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T20:38:18Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | oxford-uuid:3360a503-d419-4508-8f4e-13b15d26b8e12022-03-26T13:19:52ZApproximate subgroups of linear groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3360a503-d419-4508-8f4e-13b15d26b8e1Symplectic Elements at Oxford2010Breuillard, EGreen, BTao, TWe establish various results on the structure of approximate subgroups in linear groups such as SL_n(k) that were previously announced by the authors. For example, generalising a result of Helfgott (who handled the cases n = 2 and 3), we show that any approximate subgroup of SL_n(F_q) which generates the group must be either very small or else nearly all of SL_n(F_q). The argument generalises to other absolutely almost simple connected (and non-commutative) algebraic groups G over a finite field k. In a subsequent paper, we will give applications of this result to the expansion properties of Cayley graphs. |
| spellingShingle | Breuillard, E Green, B Tao, T Approximate subgroups of linear groups |
| title | Approximate subgroups of linear groups |
| title_full | Approximate subgroups of linear groups |
| title_fullStr | Approximate subgroups of linear groups |
| title_full_unstemmed | Approximate subgroups of linear groups |
| title_short | Approximate subgroups of linear groups |
| title_sort | approximate subgroups of linear groups |
| work_keys_str_mv | AT breuillarde approximatesubgroupsoflineargroups AT greenb approximatesubgroupsoflineargroups AT taot approximatesubgroupsoflineargroups |