Elekes-Szabó for groups, and approximate subgroups in weak general position
We show that with a suitable weak notion of general position, the Elekes-Szabó condition on the group operation of a connected complex algebraic group characterises nilpotence of the group. Along the way, we prove a Mordell-Lang result for generic finitely generated subgroups of commutative complex...
| Автори: | , , |
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| Формат: | Journal article |
| Мова: | English |
| Опубліковано: |
Alliance of Diamond Open Access Journals
2023
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| _version_ | 1826314585389400064 |
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| author | Bays, M Dobrowolski, J Zou, T |
| author_facet | Bays, M Dobrowolski, J Zou, T |
| author_sort | Bays, M |
| collection | OXFORD |
| description | We show that with a suitable weak notion of general position, the Elekes-Szabó condition on the group operation of a connected complex algebraic group characterises nilpotence of the group. Along the way, we prove a Mordell-Lang result for generic finitely generated subgroups of commutative complex algebraic groups. |
| first_indexed | 2024-03-07T08:18:24Z |
| format | Journal article |
| id | oxford-uuid:3b85d9d3-c8ae-489f-b427-23fa6bbc90bc |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:34:46Z |
| publishDate | 2023 |
| publisher | Alliance of Diamond Open Access Journals |
| record_format | dspace |
| spelling | oxford-uuid:3b85d9d3-c8ae-489f-b427-23fa6bbc90bc2024-09-18T12:21:04ZElekes-Szabó for groups, and approximate subgroups in weak general positionJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3b85d9d3-c8ae-489f-b427-23fa6bbc90bcEnglishSymplectic ElementsAlliance of Diamond Open Access Journals2023Bays, MDobrowolski, JZou, TWe show that with a suitable weak notion of general position, the Elekes-Szabó condition on the group operation of a connected complex algebraic group characterises nilpotence of the group. Along the way, we prove a Mordell-Lang result for generic finitely generated subgroups of commutative complex algebraic groups. |
| spellingShingle | Bays, M Dobrowolski, J Zou, T Elekes-Szabó for groups, and approximate subgroups in weak general position |
| title | Elekes-Szabó for groups, and approximate subgroups in weak general position |
| title_full | Elekes-Szabó for groups, and approximate subgroups in weak general position |
| title_fullStr | Elekes-Szabó for groups, and approximate subgroups in weak general position |
| title_full_unstemmed | Elekes-Szabó for groups, and approximate subgroups in weak general position |
| title_short | Elekes-Szabó for groups, and approximate subgroups in weak general position |
| title_sort | elekes szabo for groups and approximate subgroups in weak general position |
| work_keys_str_mv | AT baysm elekesszaboforgroupsandapproximatesubgroupsinweakgeneralposition AT dobrowolskij elekesszaboforgroupsandapproximatesubgroupsinweakgeneralposition AT zout elekesszaboforgroupsandapproximatesubgroupsinweakgeneralposition |