Elekes-Szab\'o for groups, and approximate subgroups in weak general position
Combinatorics
2026-04-02 v2 Logic
Abstract
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.
Cite
@article{arxiv.2107.05547,
title = {Elekes-Szab\'o for groups, and approximate subgroups in weak general position},
author = {Martin Bays and Jan Dobrowolski and Tingxiang Zou},
journal= {arXiv preprint arXiv:2107.05547},
year = {2026}
}