A local classification of some finite classical Tits geometries and chamber systems of characteristic \(\neq 3\) (Q1110807)

The author finishes the classification of locally finite classical Tits chamber systems in characteristic not 3 (that have a transitive group of automorphisms with finite chamber stabilizer) by treating the case where the characteristic is 2, the rank at least 4 and some rank 2 residue is a generalized n-gon for \(n=6\) or 8 (Theorem A): only the well-known examples occur. Together with results by Timmesfeld and the author, Theorem A yields a classification of all finite classical Tits geometries of characteristic not 3 that have a flag-transitive automorphism group (Theorem B). Much of the proof of Theorem A consists in the investigation of possible extensions of the rank 3 systems with diagram 0-0\(\equiv 0\) defined over GF(2).