On basis-transitive geometric lattices
The author considers the structure of two- and three-dimensional geometric lattices with a group of automorphisms which operates transitively both on the (unordered) bases and on the points of this lattice. He shows that - with some exceptions - all those lattices are truncations of a Boolean lattice or of an affine or a projective geometry. Thus the author generalizes a theorem of \textit{W. M. Kantor} [J. Comb. Theory, Ser. A 38, 66-74 (1985; Zbl 0559.05015)] on geometry lattices with an automorphism group transitive on ordered bases.
scientific article; zbMATH DE number 4116556