Geometric sets of permutations (Q1097511)

The permutation geometries are analogous to matroids and belong to a linear diagram in which all strokes except the last are linear spaces, while the last consists of rank 2 permutation geometries. A geometric group is a geometric set of permutations (hyperplane family in a permutation geometry) which forms a group. The present paper gives coding-type bounds and extremal results, and a detailed study of rank 2 geometric groups.