| Résume | A simple group is pseudofinite if and only if it is 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 any simple pseudofinite group G is finite-dimensional. In particular, if dim(G) = 3 then G is isomorphic to PSL(2,F) for some pseudofinite field F. In this talk, we describe the structure of finite-dimensional pseudofinite groups with dimension < 4, without using CFSG. Our results in particular prove the classification G=PSL(2,F) from the above without CFSG. This is joint work with Frank Wagner. |
