Reihentext + Finite Geometries From the reviews: "Such a vast amount of information as this book contains can only be accomplished in 375 pages by a very economical style of writing... it enables one to have a good look at the forest without being too detracted by the individual trees... The author deserves unstinting praise for the skill, energy, and perseverance which he devoted to this work. The finished product confirms what his many earlier contributions to the subject of finite geometry have already indicated, namely, that he is an undisputed leader in his field." Mathematical Reviews "Finite Geometries" is a very important area of finite mathematics characterized by an interplay of combinatorial, geometric, and algebraic ideas, in which research has been very active and intensive in recent years... makes it clear how large is the field covered by the author in his book. The material is selected most thoroughly, and the author made an effort to collect all that seems to be relevant in finite geometries for the time being... Dembowski's work will be a basic reference book of this field, and it will be considered as a base of the future research... Altogether this is a very well-produced monograph." Publicationes Mathematicae Debrecen 10, tom 16
CONTENT
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
