This dissertation describes an algorithm for constructing the basic algebra Morita equivalent to the principal block of certain group algebras. This algorithm uses the method of condensation as it is described in [Lux97]. Using an intermediate condensation subalgebra allows for the construction of the projective indecomposable modules required to realize the basic algebra. The group algebras we...

This paper is a sequel to Curtis [7], where the Held group was constructed using a 7-modular monomial representation of 3·A7, the exceptional triple cover of the alternating group A7. In this paper, a 5-modular monomial representation of 2·HS:2, a double cover of the automorphism group of the Higman–Sims group, is used to build an infinite semi-direct product P which has HN, the Harada– Norton ...

The connection between doubly transitive permutation groups G on a finite set Cl which are not doubly primitive and automorphism groups of block designs in which X = 1 has been investigated by Sims [2] and Atkinson [1]. If, for a e Q, Ga has a set of imprimitivity of size 2 then it is easy to show that G is either sharply doubly transitive or is a group of automorphisms of a non-trivial block d...

A group G has a Frobenius graphical representation (GFR) if there is simple graph ? whose full automorphism isomorphic to acting on the vertices as group. In particular, any with GFR and Cayley graph. By very recent results of Spiga, exists function f such that finite complement H | > (| |) then admits GFR. This paper provides an infinite family graphs admit GFRs despite not meeting Spiga’s ...

Two class association schemes consist of either strongly regular graphs (SRG) or doubly regular tournaments (DRT). We construct self-dual codes from the adjacency matrices of these schemes. This generalizes the construction of Pless ternary Symmetry codes, Karlin binary Double Circulant codes, Calderbank and Sloane quaternary double circulant codes, and Gaborit Quadratic Double Circulant codes ...

The inequality of Higman for generalized quadrangles of order (s, t) with s > 1 states that t ≤ s. We will generalize this by proving that the intersection number ci of a regular near 2d-gon of order (s, t) with s > 1 satisfies the tight bound ci ≤ (s − 1)/(s − 1), and we give properties in case of equality. It is known that hemisystems in generalized quadrangles meeting the Higman bound induce...

Charles Sims suggested that this should be true in [11]. Much work has been done since—see for instance the papers of Thompson [15], Wielandt [17] and Knapp [6]. In particular, Thompson proved in [15] the existence of a function g such that for any G as above there is a prime p and a normal p-subgroup P of G with |Ga: P\ ^ g(d). Nevertheless, the conjecture has remained open until now. As a con...

article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this work, we study a generalization of the concept of modules by considering more general setting which is called OG-diagrams. We use Higman criteria and relative projectivity as the main tool...

s of invited talks Metamorphoses of graph designs Elizabeth J. Billington University of Queensland A lambda-fold graph design, or G-design of order n, is an edge-disjoint decomposition of a λ-fold complete graph, λKn, into isomorphic copies of some graph G. (Here λKn denotes the graph on n vertices with precisely λ edges between every pair of vertices.) Let H be a subgraph of G. A metamorphosis...