Diagram Geometry

ranging from the construction of diagram geometries on the basis of known groups and a system of their subgroups to the classification of all geometries pertaining to a given diagram. Although quite a few diagrams have been found for ...

Diagram Geometry

This book provides a self-contained introduction to diagram geometry. Tight connections with group theory are shown. It treats thin geometries (related to Coxeter groups) and thick buildings from a diagrammatic perspective. Projective and affine geometry are main examples. Polar geometry is motivated by polarities on diagram geometries and the complete classification of those polar geometries whose projective planes are Desarguesian is given. It differs from Tits' comprehensive treatment in that it uses Veldkamp's embeddings. The book intends to be a basic reference for those who study diagram geometry. Group theorists will find examples of the use of diagram geometry. Light on matroid theory is shed from the point of view of geometry with linear diagrams. Those interested in Coxeter groups and those interested in buildings will find brief but self-contained introductions into these topics from the diagrammatic perspective. Graph theorists will find many highly regular graphs. The text is written so graduate students will be able to follow the arguments without needing recourse to further literature. A strong point of the book is the density of examples.

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Diagram Geometry
Language: en
Pages: 594
Authors: Francis Buekenhout, Arjeh M. Cohen
Categories: Mathematics
Type: BOOK - Published: 2013-01-26 - Publisher: Springer Science & Business Media

This book provides a self-contained introduction to diagram geometry. Tight connections with group theory are shown. It treats thin geometries (related to Coxeter groups) and thick buildings from a diagrammatic perspective. Projective and affine geometry are main examples. Polar geometry is motivated by polarities on diagram geometries and the complete
Geometries and Groups
Language: en
Pages: 542
Authors: M. Aschbacher, A.M. Cohen, W.M. Kantor
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

The workshop was set up in order to stimulate the interaction between (finite and algebraic) geometries and groups. Five areas of concentrated research were chosen on which attention would be focused, namely: diagram geometries and chamber systems with transitive automorphism groups, geometries viewed as incidence systems, properties of finite groups
Projective Geometry
Language: en
Pages: 258
Authors: Albrecht Beutelspacher, Beutelspacher Albrecht, Ute Rosenbaum
Categories: Mathematics
Type: BOOK - Published: 1998-01-29 - Publisher: Cambridge University Press

A textbook on projective geometry that emphasises applications in modern information and communication science.
Geometry of Sporadic Groups: Volume 1, Petersen and Tilde Geometries
Language: en
Pages: 424
Authors: A. A. Ivanov
Categories: Mathematics
Type: BOOK - Published: 1999-06-17 - Publisher: Cambridge University Press

Important monograph on finite group theory.
Buildings and the Geometry of Diagrams
Language: en
Pages: 282
Authors: Luigi A. Rosati
Categories: Mathematics
Type: BOOK - Published: 2006-11-14 - Publisher: Springer

Books about Buildings and the Geometry of Diagrams