On generic and supertight automorphisms
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915949050855424 |
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| author | Kowalski, Piotr Kowalski, Pınar Uğurlu |
| author_facet | Kowalski, Piotr Kowalski, Pınar Uğurlu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20415 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On generic and supertight automorphisms Kowalski, Piotr Kowalski, Pınar Uğurlu Group Theory Logic 03C45, 03C60, 20G99 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. |
| title | On generic and supertight automorphisms |
| topic | Group Theory Logic 03C45, 03C60, 20G99 |
| url | https://arxiv.org/abs/2604.20415 |