Apartments in flag transitive geometries (Q1345912)

The author assumes that an apartment \(A\) of a finite Tits geometry \(\Gamma\) is a thin geometry such that the stabiliser of \(A\) in \(\text{Aut} (\Gamma)\) acts transitively on \(A\). So he proves that a finite classical flag-transitive Tits geometry is a building if it admits an apartment and if it has buildings as every rank 3 residue. Moreover the geometries \(\Gamma\) defined by a parabolic system of type \(M_{24}\) for the group \(\text{Aut} (\Gamma)\) are studied.