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arXiv · 2604.20415

On generic and supertight automorphisms

Piotr Kowalski·Pınar Uğurlu Kowalski
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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 $\mathrm{PGL}_2(K)$ and generic automorphisms of the underlying field $K$. 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.

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Piotr Kowalski, Pınar Uğurlu Kowalski. 2026-04-22. On generic and supertight automorphisms. https://arxiv.org/abs/2604.20415

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