Elekes-Szabó for groups, and approximate subgroups in weak general position
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866912993744257024 |
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| author | Bays, Martin Dobrowolski, Jan Zou, Tingxiang |
| author_facet | Bays, Martin Dobrowolski, Jan Zou, Tingxiang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_05547 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Elekes-Szabó for groups, and approximate subgroups in weak general position Bays, Martin Dobrowolski, Jan Zou, Tingxiang Combinatorics Logic 05E15 (Primary) 03C98, 22E25, 14K05 (Secondary) 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. |
| title | Elekes-Szabó for groups, and approximate subgroups in weak general position |
| topic | Combinatorics Logic 05E15 (Primary) 03C98, 22E25, 14K05 (Secondary) |
| url | https://arxiv.org/abs/2107.05547 |