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arXiv · 2107.05547

Elekes-Szabó for groups, and approximate subgroups in weak general position

Martin Bays·Jan Dobrowolski·Tingxiang Zou
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Abstract

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.

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Martin Bays, Jan Dobrowolski, Tingxiang Zou. 2023-05-26. Elekes-Szabó for groups, and approximate subgroups in weak general position. https://doi.org/10.19086/da.77361

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