Advances in Finite Geometries and Designs de J. W. P. Hirschfeld

Advances in Finite Geometries and Designs: Proceedings of the Third Isle of Thorns Conference 1990

J. W. P. Hirschfeld

D. R. Hughes

J. A. Thas

This volume comprises papers presented at the Third Isle of Thorns Conference on Finite Geometries and Designs. The papers explore the structure and associated incidence structures of Galois geometries, and their related automorphism groups.Amongst the main topics covered are generalized quadrangles and n-gons, groups acting on geometries, linear spaces, partial geometries, diagram geometries, non-Desarguesian planes, strongly regular graphs, and designs.

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Preface; Table of contents; Introduction; L. Bader: Flocks of cones and generalized hexagons; L.M. Batten and J.M.N. Brown: Group partitions, affine spaces and translation groups; A. Blokhuis and F. Mazzocca: On maximal sets of nuclei in PG(2,q) and quasi-odd sets in AG(2,q); A. Blokhuis, A.R. Calderbank, K. Metsch and A. Seress: An embedding theorem for partial linear spaces; A.E. Brouwer: A non-degenerate generalized quadrangle with lines of size four is finite; J.M.N. Brown: On abelian collineation groups of finite projective planes; F. Buekenhout: More geometry for Hering's 3 :SL(2,13); A.M. Cohen: Presentations for certain finite quaternionic relection groups; B.N. Cooperstein and E.E. Shult: Geometric hyperplanes of embeddable Lie incidence geometries; F. De Clerck, A. Del Fra, and D. Ghinelli: Pointsets in partial geometries; A. Del Fra, D. Ghinelli, and A. Pasini: One diagram for many geometries; M.J. de Resmini: On an exceptional semi-translation plane; W.HL Haemers, D.G. Higman, and S.A. Hobart: Strongly regular graphs induced by polarities of symmetric designs; J.W.P. Hirschfeld and Tzonyi: A Problem on squares in a finite field and its application to geometry; C. Ho and A. Goncalves: On totally irregular simple collineation groups; D.R. Hughes: On some rank 3 partial geometries; D. Jungnickel and V.D. Tonchev: Intersection numbers of quasi-multiples of symmetric designs; H. kaneta and T. Maruta: The discriminant of a cubic curve; W.M. Kantor: Automorphism groups of some generalized quadrangles; G. Korchmaros: Collineation groups of (q + t, t)-arcs of type (0,2,t) in a Desarguesian plane of order q; Y. Liu and Z. Wan: Pseudo-symplectic geometries over finite fields of characteristic two; S. Lowe: Solutions of quadratic equations in a groupring and partial addition sets; G. Lunardon: A remark on the derivation of flocks; T. Maruta: A geometric approach to semi-cyclic codes; G. Mason: Remarks on non-associative Galois theory; G.E. Moorhouse: Codes of nets with translations; C.M. O'Keefe, T Penttila, and C.M. Praeger: Stabilizers of hyperovals in PG(2, 32); J. Siemons and B. Webb: On a problem of Wielandt and a question by Dembowski; E. Spence: (40, 13,4)-designs derived from strongly regular graphs; L. Storme and J.A. Thas: Generalized Reed-Solomon codes and normal rational curves: an improvement of results by Seroussi and Roth; H. Van Maldeghem: Common characterizations of the finite Moufang polygons; J.F. Voloch: Complete arcs in Galois planes of non-square order; F. Wettl: Internal nuclei of k-sets in finite projective spaces of three dimensions; P.R. Wild: Menon difference sets and relative difference sets; List of Talks; List of Participants.