1st Edition

Finite Geometries

By Baker Copyright 1985

    This book is a compilation of the papers presented at the conference in Winnipeg on the subject of finite geometry in 1984. It covers different fields in finite geometry: classical finite geometry, the geometry of finite planes, geometric structures and the theory of translation planes.

    1. A Brief Summary of the Geometry of Sets 2. Sets of Type (1, k, k + 1) in Projective Planes of Order n 3. Embedding Finite Planar Spaces in Projective Spaces 4. The Locally Icosahedral Graphs 5. Locally Polyhedral Graphs 6. Four Lectures on Projective Geometry 7. Harmonic Ovals of Even Order 8. Exterior Sets with Respect to the Hyperbolic Quadric in PG(2n - 1, q) 9. Finite 2-Homogeneous Linear Spaces 10. A Generalized Modification of the Von Staudt Theory of Imaginary Elements 11. Linear Spaces and Groups 12. Maximal (k + 1)-Cliques, That Carry Maximal k-Cliques 13. Spreads Obtained from Ovoidal Fibrations 14. Two New Sporadic Doubly Transitive Linear Spaces 15. A Class of Rank (3,2)-Planes 16. Near-Field-Like Planes 17. Translation Planes of Order n Which Admit a Collineation Group of Order n 18. Compatibility of Baer and Elation Groups in Translation Planes 19. Sporadic Simple Groups Acting on Finite Translation Planes 20. Flag-Transitive Planes 21. Generating Sets in Finite Projective Planes 22. A Search for a Non-Desarguesian Plane of Prime Order 23. Configuration Theorems on Cubic Quasigroups 24. Some Remarks on Covers and Apartments 25. Hyperovals and Generalized Quadrangles 26. A Characterization of the Set of Lines Either Tangent to or Lying on a Nonsingular Quadric in PG(4,q), q Odd 27. Extensions of Regular Complexes 28. On Sets of given Type in a Steiner System 29. The k-Sets of PG(r,q) from the Character Point of View 30. Circle Geometries and Generalized Quadrangles 31. The Projective Geometry of Rigid Frameworks


    Catherine Anne Baker