Linear Approximate Groups
This is an informal announcement of results to be described and proved in detail in a paper to appear. We give various results on the structure of approximate subgroups in linear groups such as $\SL_n(k)$. For example, generalising a result of Helfgott (who handled the cases $n = 2$ and 3), we show...
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| Format: | Journal article |
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2010
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| _version_ | 1826271287111057408 |
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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 | This is an informal announcement of results to be described and proved in detail in a paper to appear. We give various results on the structure of approximate subgroups in linear groups such as $\SL_n(k)$. 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 is valid for all Chevalley groups $G(\F_q)$. |
| first_indexed | 2024-03-06T21:54:18Z |
| format | Journal article |
| id | oxford-uuid:4c631ee3-d7d5-43fb-a145-9c0dc2a330fb |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:54:18Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | oxford-uuid:4c631ee3-d7d5-43fb-a145-9c0dc2a330fb2022-03-26T15:49:03ZLinear Approximate GroupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:4c631ee3-d7d5-43fb-a145-9c0dc2a330fbSymplectic Elements at Oxford2010Breuillard, EGreen, BTao, TThis is an informal announcement of results to be described and proved in detail in a paper to appear. We give various results on the structure of approximate subgroups in linear groups such as $\SL_n(k)$. 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 is valid for all Chevalley groups $G(\F_q)$. |
| spellingShingle | Breuillard, E Green, B Tao, T Linear Approximate Groups |
| title | Linear Approximate Groups |
| title_full | Linear Approximate Groups |
| title_fullStr | Linear Approximate Groups |
| title_full_unstemmed | Linear Approximate Groups |
| title_short | Linear Approximate Groups |
| title_sort | linear approximate groups |
| work_keys_str_mv | AT breuillarde linearapproximategroups AT greenb linearapproximategroups AT taot linearapproximategroups |