Product decompositions in finite simple groups
We propose a general conjecture on decompositions of finite simple groups as products of conjugates of an arbitrary subset. We prove this conjecture for bounded subsets of arbitrary finite simple groups, and for large subsets of groups of Lie type of bounded rank. Some of our arguments apply recent...
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| Format: | Journal article |
| Language: | English |
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2011
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| _version_ | 1826342845564321792 |
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| author | Liebeck, M Nikolov, N Shalev, A |
| author_facet | Liebeck, M Nikolov, N Shalev, A |
| author_sort | Liebeck, M |
| collection | OXFORD |
| description | We propose a general conjecture on decompositions of finite simple groups as products of conjugates of an arbitrary subset. We prove this conjecture for bounded subsets of arbitrary finite simple groups, and for large subsets of groups of Lie type of bounded rank. Some of our arguments apply recent advances in the theory of growth in finite simple groups of Lie type, and provide a variety of new product decompositions of these groups. |
| first_indexed | 2024-03-07T05:51:01Z |
| format | Journal article |
| id | oxford-uuid:e8e1f62d-fda1-45d8-b8f3-06a47c7c8a7a |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:51:01Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:e8e1f62d-fda1-45d8-b8f3-06a47c7c8a7a2022-03-27T10:50:05ZProduct decompositions in finite simple groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e8e1f62d-fda1-45d8-b8f3-06a47c7c8a7aEnglishSymplectic Elements at Oxford2011Liebeck, MNikolov, NShalev, AWe propose a general conjecture on decompositions of finite simple groups as products of conjugates of an arbitrary subset. We prove this conjecture for bounded subsets of arbitrary finite simple groups, and for large subsets of groups of Lie type of bounded rank. Some of our arguments apply recent advances in the theory of growth in finite simple groups of Lie type, and provide a variety of new product decompositions of these groups. |
| spellingShingle | Liebeck, M Nikolov, N Shalev, A Product decompositions in finite simple groups |
| title | Product decompositions in finite simple groups |
| title_full | Product decompositions in finite simple groups |
| title_fullStr | Product decompositions in finite simple groups |
| title_full_unstemmed | Product decompositions in finite simple groups |
| title_short | Product decompositions in finite simple groups |
| title_sort | product decompositions in finite simple groups |
| work_keys_str_mv | AT liebeckm productdecompositionsinfinitesimplegroups AT nikolovn productdecompositionsinfinitesimplegroups AT shaleva productdecompositionsinfinitesimplegroups |