Finite geometries/
Peter Dembowski
- New York: Springer, 1997.
- 375
1. Basic concepts.- 1.1 Finite incidence structures.- 1.2 Incidence preserving maps.- 1.3 Incidence matrices.- 1.4 Geometry of finite vector spaces.- 2. Designs.- 2.1 Combinatorial properties.- 2.2 Embeddings and extensions.- 2.3 Automorphisms of designs.- 2.4 Construction of designs.- 3. Projective and affine planes.- 3.1 General results.- 3.2 Combinatorics of finite planes.- 3.3 Correlations and polarities.- 3.4 Projectivities.- 4. Collineations of finite planes.- 4.1 Fixed elements and orders.- 4.2 Collineation groups.- 4.3 Central collineations.- 4.4 Groups with few orbits.- 5. Construction of finite planes.- 5.1 Algebraic representations.- 5.2 Planes of type IV.- 5.3 Planes of type V.- 5.4 Planes of types I and II.- 6. Inversive planes.- 6.1 General definitions and results.- 6.2 Combinatorics of finite inversive planes.- 6.3 Automorphisms.- 6.4 The known finite models.- 7. Appendices.- 7.1 Association schemes and partial designs.- 7.2 Hjelmslev planes.- 7.3 Generalized polygons.- 7.4 Finite semi-planes.- Dictionary.- Special notations.