In this note we will generalize the Higman-Haemers inequalities for generalized polygons to thick regular near polygons.

A construction of Tits is used to cast the argument of Kilmoyer-Solomon and Higman proving the Feit-Higman theorem in the context of tactical configurations. An analog of a result of Cvetkovic shows what combinatorial data is needed to determine the representations associated with a given configuration. The possible representations fall into three types. A bound is given for the size of certain...

It has been known for some time that the Higman-Sims graph can be decomposed into the disjoint union of two Hoffman-Singleton graphs. In this paper we establish that the Higman-Sims graph can be edge decomposed into the disjoint union of 5 double-Petersen graphs, each on 20 vertices. It is shown that in fact this can be achieved in 36960 distinct ways. It is also shown that these different ways...

There does not exist an isomorphism-invariant Borel version of the Higman-Neumann-Neumann Embedding Theorem.

All linear codes of length 100 over a field F which admit the Higman-Sims simple group HS in its rank 3 representation are determined. By group representation theory it is proved that they can all be understood as submodules of the permutation module FΩ where Ω denotes the vertex set of the Higman-Sims graph. This module is semisimple if charF 6= 2, 5 and absolutely indecomposable otherwise. Al...