Author | Dembowski, Peter. author |
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Title | Finite Geometries [electronic resource] : Reprint of the 1968 Edition / by Peter Dembowski |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1997 |
Connect to | http://dx.doi.org/10.1007/978-3-642-62012-6 |
Descript | XI, 379 p. online resource |
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