Finite-dimensional pseudofinite groups of small dimension, without CFSG
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916521432842240 |
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| author | Karhumäki, Ulla Wagner, Frank Olaf |
| author_facet | Karhumäki, Ulla Wagner, Frank Olaf |
| contents | Any simple pseudofinite group G is known to be isomorphic to a (twisted) Chevalley group over a pseudofinite field. This celebrated result mostly follows from the work of Wilson in 1995 and heavily relies on the classification of finite simple groups (CFSG). It easily follows that G is finite-dimensional with additive and fine dimension and, in particular, that if dim(G)=3 then G is isomorphic to PSL(2,F) for some pseudofinite field F. We describe pseudofinite finite-dimensional groups when the dimension is fine, additive and \<4 and, in particular, show that the classification G isomorphic to PSL(2,F) is independent from CFSG. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11484 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite-dimensional pseudofinite groups of small dimension, without CFSG Karhumäki, Ulla Wagner, Frank Olaf Group Theory Logic Any simple pseudofinite group G is known to be isomorphic to a (twisted) Chevalley group over a pseudofinite field. This celebrated result mostly follows from the work of Wilson in 1995 and heavily relies on the classification of finite simple groups (CFSG). It easily follows that G is finite-dimensional with additive and fine dimension and, in particular, that if dim(G)=3 then G is isomorphic to PSL(2,F) for some pseudofinite field F. We describe pseudofinite finite-dimensional groups when the dimension is fine, additive and \<4 and, in particular, show that the classification G isomorphic to PSL(2,F) is independent from CFSG. |
| title | Finite-dimensional pseudofinite groups of small dimension, without CFSG |
| topic | Group Theory Logic |
| url | https://arxiv.org/abs/2408.11484 |