Elekes-Szab\'o for groups, and approximate subgroups in weak general position

Elekes-Szab\'o for groups, and approximate subgroups in weak general position

We show that with a suitable weak notion of general position, the Elekes-Szab\'o 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 c...

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Hauptverfasser: Bays, Martin, Dobrowolski, Jan, Zou, Tingxiang
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Combinatorics
Mathematics - Logic
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Zusammenfassung:We show that with a suitable weak notion of general position, the Elekes-Szab\'o 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.
DOI:10.48550/arxiv.2107.05547