Random unipotent Sylow subgroups of groups of Lie type of bounded rank
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911137669316608 |
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| author | Skresanov, Saveliy V. |
| author_facet | Skresanov, Saveliy V. |
| contents | In 2001 Liebeck and Pyber showed that a finite simple group of Lie type is a product of $ 25 $ carefully chosen unipotent Sylow subgroups. Later, in a series of works it was shown that $ 4 $ unipotent Sylow subgroups suffice. We prove that if the rank of a finite simple group of Lie type $ G $ is bounded, then $ G $ is a product of $ 11 $ random unipotent Sylow subgroups with probability tending to $ 1 $ as $ |G| $ tends to infinity. An application of the result to finite linear groups is given. The proofs do not depend on the classification of finite simple groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15772 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Random unipotent Sylow subgroups of groups of Lie type of bounded rank Skresanov, Saveliy V. Group Theory 20D06 (Primary) 20D20, 20P05 (Secondary) In 2001 Liebeck and Pyber showed that a finite simple group of Lie type is a product of $ 25 $ carefully chosen unipotent Sylow subgroups. Later, in a series of works it was shown that $ 4 $ unipotent Sylow subgroups suffice. We prove that if the rank of a finite simple group of Lie type $ G $ is bounded, then $ G $ is a product of $ 11 $ random unipotent Sylow subgroups with probability tending to $ 1 $ as $ |G| $ tends to infinity. An application of the result to finite linear groups is given. The proofs do not depend on the classification of finite simple groups. |
| title | Random unipotent Sylow subgroups of groups of Lie type of bounded rank |
| topic | Group Theory 20D06 (Primary) 20D20, 20P05 (Secondary) |
| url | https://arxiv.org/abs/2501.15772 |