Year: 2025
Type: article
Abstract: 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 groups of fine and additive dimension ⩽ 3 and, in particular, show that the classification G ≅ PSL 2 ( F ) is independent of CFSG.
Source: Confluentes Mathematici
DOI: 10.5802/cml.100
Authors: Ulla Karhumäki, Frank O. Wagner
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4401717119