On generic and supertight automorphisms
Group Theory
2026-04-23 v1 Logic
Abstract
We show that generic automorphisms of stable groups are supertight in a strong sense. In particular, we obtain the existence of supertight automorphisms. We also answer a question concerning the relationship between supertight automorphisms of and generic automorphisms of the underlying field . Moreover, we provide partial evidence-already suggested by Hrushovski-toward the principle that ``fixed points are pseudofinite'' in the setting of generic automorphisms of simple groups of finite Morley rank.
Cite
@article{arxiv.2604.20415,
title = {On generic and supertight automorphisms},
author = {Piotr Kowalski and Pınar Uğurlu Kowalski},
journal= {arXiv preprint arXiv:2604.20415},
year = {2026}
}