Elekes-Szabó for groups, and approximate subgroups in weak general position - Bays, M; Dobrowolski, J; Zou, T (Alliance of Diamond Open Access Journals, 2023)
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.