Automorphisms of B-Geometries

(B)-Geometries are incidence structures arising from permutation sets. The automorphism groups of (B)-Geometries are studied in the paper. In certain cases they yield examples of inversive planes and sublplanes which are embedded in Minkowski planes. The automorphism groups of (B)-geometries associated with both the finite affine semilinear group and the finite projective semilineart group, in their representation on the points of the finite projective and affine line, are described.