Minimal operations over permutation groups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911158488793088 |
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| author | Marimon, Paolo Pinsker, Michael |
| author_facet | Marimon, Paolo Pinsker, Michael |
| contents | We classify the possible types of minimal operations above an arbitrary permutation group. Above the trivial group, a theorem of Rosenberg yields that there are five types of minimal operations. We show that above any non-trivial permutation group there are at most four such types. Indeed, except above Boolean groups acting freely on a set, there are only three. In particular, this is the case for oligomorphic permutation groups, for which we improve a result of Bodirsky and Chen by showing one of the types in their classification does not exist. Building on these results, we answer three questions of Bodirsky that were previously open. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22060 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimal operations over permutation groups Marimon, Paolo Pinsker, Michael Rings and Algebras Group Theory Logic 08A40, 20B05, 08A70, 03C05, 20B07, 20M20 We classify the possible types of minimal operations above an arbitrary permutation group. Above the trivial group, a theorem of Rosenberg yields that there are five types of minimal operations. We show that above any non-trivial permutation group there are at most four such types. Indeed, except above Boolean groups acting freely on a set, there are only three. In particular, this is the case for oligomorphic permutation groups, for which we improve a result of Bodirsky and Chen by showing one of the types in their classification does not exist. Building on these results, we answer three questions of Bodirsky that were previously open. |
| title | Minimal operations over permutation groups |
| topic | Rings and Algebras Group Theory Logic 08A40, 20B05, 08A70, 03C05, 20B07, 20M20 |
| url | https://arxiv.org/abs/2410.22060 |