Tits Buildings and the Model Theory of Groups

doi:10.1017/CBO9780511549786

This volume contains selected papers by leading researchers from the international conference entitled Tits Buildings and the Model Theory of Groups, held in Würzburg in 2000. The first part of the book provides a general introduction to many aspects of buildings and their geometries, based on short lecture courses given at the conference. The rest of the book comprises survey and research articles on model theoretic results and techniques, showing the vitality and richness of these branches of mathematics. Among the most fruitful techniques, amalgamation constructions à la Hrushovski are explained and classified as they continue to play an important role both in model theory and geometry. The articles succeed in demonstrating the close connection between geometry, group theory and model theory. The book will be invaluable to graduate students as well as experienced researchers working in these areas of mathematics.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-v
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Preface
pp vi-viii
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List of speakers and talks
pp ix-x
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Basics on buildings
pp 1-22
- By Theo Grundhöfer, Würzburg
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An introduction to generalized polygons
pp 23-58
- By Hendrik Van Maldeghem, Department of Pure Mathematics and Computer Algebra Ghent University Galglaan 2, 9000 Gent Belgium
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Buildings and classical groups
pp 59-102
- By Linus Kramer, Mathematisches Institut, Universität Würzburg Am Hubland, D–97074 Würzburg, Germany
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Twin buildings
pp 103-118
- By Bernhard Mühlherr, Fachbereich Mathematik Universität Dortmund 44221 Dortmund, Germany
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Twin trees and twin buildings
pp 119-138
- By Mark Ronan, Chicago
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Simple groups of finite Morley rank of even type
pp 139-172
- By Tuna Altinel, Institut Girard Desargues UPRES-A 5028 Mathématiques Batiment 101 (mathématiques) Université Claude Bernard Lyon-1 43 blvd du 11 novembre 1918 69622 Villeurbanne CEDEX, France
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BN-pairs and groups of finite Morley rank
pp 173-184
- By Katrin Tent, Mathematisches Institut Universität Würzburg Am Hubland, 97074 Würzburg, Germany
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CM-trivial stable groups
pp 185-194
- By Andreas Baudisch, Berlin
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Amalgames de Hrushovski: Une tentative de classification
pp 195-214
- By Bruno Poizat, Institut Girard Desargues, Mathématiques, bâtiment 101, Université Claude Bernard (Lyon-1), 43, boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France
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Rank and homogeneous structures
pp 215-234
- By John Baldwin, Department of Mathematics, Statistics and Computer Science University of Illinois at Chicago
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Constructions of semilinear towers of Steiner systems
pp 235-278
- By Keith Johnson, 116 Kirkstall Hill, Leeds, England
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Introduction to the Lascar Group
pp 279-298
- By Martin Ziegler, Freiburg
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Tits Buildings and the Model Theory of Groups

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Contents

Frontmatter
pp i-iv

Contents
pp v-v

Preface
pp vi-viii

List of speakers and talks
pp ix-x

Basics on buildings
pp 1-22

An introduction to generalized polygons
pp 23-58

Buildings and classical groups
pp 59-102

Twin buildings
pp 103-118

Twin trees and twin buildings
pp 119-138

Simple groups of finite Morley rank of even type
pp 139-172

BN-pairs and groups of finite Morley rank
pp 173-184

CM-trivial stable groups
pp 185-194

Amalgames de Hrushovski: Une tentative de classification
pp 195-214

Rank and homogeneous structures
pp 215-234

Constructions of semilinear towers of Steiner systems
pp 235-278

Introduction to the Lascar Group
pp 279-298

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