Intertwining automorphisms in finite incidence structures (Q1823304)

The linear representations of a group acting on a finite incidence structure (P,B;I) (where P: points, B: blocks; I: incidence) are studied and known results reviewed. Two results: Under some `nondegeneracy conditions' for the point-adjacency matrix, the linear representation related to P occurs in the one related to B. If the rank of the incidence matrix over \({\mathbb{R}}\) equals the order of P, then the permutation rank on P is bounded by the one on B.