Finite Geometries

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Springer Science & Business Media, 1997 - Mathematics - 375 pages
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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.
 

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Contents

1 Basic concepts
1
12 Incidence preserving maps
8
13 Incidence matrices
17
14 Geometry of finite vector spaces
23
2 Designs
56
22 Embeddings and extensions
69
23 Automorphisms of designs
78
24 Construction of designs
92
52 Planes of type IV
228
53 Planes of type V
236
54 Planes of types I and II
246
6 Inversive planes
252
62 Combinatorics of finite inversive planes
262
63 Automorphisms
268
64 The known finite models
273
7 Appendices
281

3 Projective and affine planes
115
32 Combinatorics of finite planes
137
33 Correlations and polarities
151
34 Projectivities
157
4 Collineations of finite planes
169
42 Collineation groups
178
43 Central collineations
187
44 Groups with few orbits
207
5 Construction of finite planes
219
72 Hjelmslev planes
291
73 Generalized polygons
300
74 Finite semiplanes
305
Bibliography
318
Dictionary
367
Special notations
369
Index
371
Copyright

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About the author (1997)

Biography of Peter Dembowski

Peter Dembowski was born in Berlin on April 1, 1928. After studying mathematics at the University of Frankfurt am Main, he pursued his graduate studies at Brown University and at the University of Illinois, mainly with Reinhold 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 Tübingen.

Dembowski taught at the universities of Frankfurt and Tübingen and - as visiting professor - in London (Queen Mary College), Rome, Madison, WI, and Chicago, IL.

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 also left its trace in neigh-bouring areas.

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