Finite geometries
Author(s)
Bibliographic Information
Finite geometries
（Classics in mathematics）
Springer, c1997
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Note
"Reprint of the 1968 edition."
"Originally published as vol. 44 of the Ergebnisse der Mathematik und ihrer Grenzgebiete"
Includes bibliographical references (p. [318]-370) and index
Description and Table of Contents
Description
Peter Dembowski was born in Berlin on April 1, 1928. After studying mathematics at the University of Frankfurt of Main, he pursued his graduate studies at Brown Unviersity and the University of Illinois, mainly with R. Baer. Dembowski returned to Frankfurt in 1956. Shortly before his premature death in January 1971, he had been appointed to a chair at the University of Tuebingen. Dembowski taught at the universities of Frankfurt and Tuebingen and - as visiting Professor - in London (Queen Mary College), Rome, and Madison, WI. Dembowski's chief research interest lay in the connections between finite geometries and group theory. His book "Finite Geometries" brought together essentially all that was known at that time about finite geometrical structures, including key results of the author, in a unified and structured perspective. This book became a standard reference as soon as it appeared in 1968. It influenced the expansion of combinatorial geometric research, and left its trace also in neighbouring areas.
Table of Contents
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.
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