Decent actions of groups on restricted products
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915955395788800 |
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| author | Karpinski, Chris |
| author_facet | Karpinski, Chris |
| contents | An action of a group $G$ on a set $X$ is called ``decent'' if every subgroup of $G$ with a finite orbit in $X$ fixes a point in $X$ and every finitely generated subgroup of $G$ such that every element of the subgroup fixes a point of $X$ must itself have a global fixed point. In this article, we study conditions on when actions of groups on restricted products are ``decent''. We prove that the action of the automorphism group of a restricted product with base space the projective plane $\mathbb{P}^2(k)$ over a field $k$ is decent, generalizing a result of Lonjou--Przytycki--Urech. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22635 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Decent actions of groups on restricted products Karpinski, Chris Group Theory Algebraic Geometry Dynamical Systems 14E07, 20F65, 37F10 An action of a group $G$ on a set $X$ is called ``decent'' if every subgroup of $G$ with a finite orbit in $X$ fixes a point in $X$ and every finitely generated subgroup of $G$ such that every element of the subgroup fixes a point of $X$ must itself have a global fixed point. In this article, we study conditions on when actions of groups on restricted products are ``decent''. We prove that the action of the automorphism group of a restricted product with base space the projective plane $\mathbb{P}^2(k)$ over a field $k$ is decent, generalizing a result of Lonjou--Przytycki--Urech. |
| title | Decent actions of groups on restricted products |
| topic | Group Theory Algebraic Geometry Dynamical Systems 14E07, 20F65, 37F10 |
| url | https://arxiv.org/abs/2604.22635 |