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Strongly Regular Graphs
This monograph on strongly regular graphs is an invaluable reference for anybody working in algebraic combinatorics.
Finite Geometries, Groups, and Computation
This volume is the proceedings of a conference on Finite Geometries, Groups, and Computation that took place on September 4-9, 2004, at Pingree Park, Colorado (a campus of Colorado State University). Not accidentally, the conference coincided with the 60th birthday of William Kantor, and the topics relate to his major research areas. Participants were encouraged to explore the deeper interplay between these fields. The survey papers by Kantor, O'Brien, and Penttila should serve to introduce both students and the broader mathematical community to these important topics and some of their connections while the volume as a whole gives an overview of current developments in these fields.
Algebraic Combinatorics and the Monster Group
Covering, arguably, one of the most attractive and mysterious mathematical objects, the Monster group, this text strives to provide an insightful introduction and the discusses the current state of the field. The Monster group is related to many areas of mathematics, as well as physics, from number theory to string theory. This book cuts through the complex nature of the field, highlighting some of the mysteries and intricate relationships involved. Containing many meaningful examples and a manual introduction to the computer package GAP, it provides the opportunity and resources for readers to start their own calculations. Some 20 experts here share their expertise spanning this exciting field, and the resulting volume is ideal for researchers and graduate students working in Combinatorial Algebra, Group theory and related areas.
Groups and Geometries
On September 1-7, 1996 a conference on Groups and Geometries took place in lovely Siena, Italy. It brought together experts and interested mathematicians from numerous countries. The scientific program centered around invited exposi tory lectures; there also were shorter research announcements, including talks by younger researchers. The conference concerned a broad range of topics in group theory and geometry, with emphasis on recent results and open problems. Special attention was drawn to the interplay between group-theoretic methods and geometric and combinatorial ones. Expanded versions of many of the talks appear in these Proceedings. This volume is intended to provide a stimulating co...
Buildings, Finite Geometries and Groups
This is the Proceedings of the ICM 2010 Satellite Conference on “Buildings, Finite Geometries and Groups” organized at the Indian Statistical Institute, Bangalore, during August 29 – 31, 2010. This is a collection of articles by some of the currently very active research workers in several areas related to finite simple groups, Chevalley groups and their generalizations: theory of buildings, finite incidence geometries, modular representations, Lie theory, etc. These articles reflect the current major trends in research in the geometric and combinatorial aspects of the study of these groups. The unique perspective the authors bring in their articles on the current developments and the major problems in their area is expected to be very useful to research mathematicians, graduate students and potential new entrants to these areas.
Finite Geometry and Combinatorics
Included here are articles from many of the leading practitioners in the field, including, for the first time, several distinguished Russian mathematicians. Many of the papers contain important new results, and the growing use of computer algebra packages in this area is also demonstrated.
Finite Geometries
When? These are the proceedings of Finite Geometries, the Fourth Isle of Thorns Conference, which took place from Sunday 16 to Friday 21 July, 2000. It was organised by the editors of this volume. The Third Conference in 1990 was published as Advances in Finite Geometries and Designs by Oxford University Press and the Second Conference in 1980 was published as Finite Geometries and Designs by Cambridge University Press. The main speakers were A. R. Calderbank, P. J. Cameron, C. E. Praeger, B. Schmidt, H. Van Maldeghem. There were 64 participants and 42 contributions, all listed at the end of the volume. Conference web site http://www. maths. susx. ac. uk/Staff/JWPH/ Why? This collection of 2...
Symmetry in Finite Generalized Quadrangles
This monograph classifies finite generalized quadrangles by symmetry, generalizing the celebrated Lenz-Barlotti classification for projective planes. The book introduces combinatorial, geometrical and group-theoretical concepts that arise in the classification and in the general theory of finite generalized quadrangles, including automorphism groups, elation and translation generalized quadrangles, generalized ovals and generalized ovoids, span-symmetric generalized quadrangles, flock geometry and property (G), regularity and nets, split BN-pairs of rank 1, and the Moufang property.
Translation Generalized Quadrangles
Translation generalized quadrangles play a key role in the theory of generalized quadrangles, comparable to the role of translation planes in the theory of projective and affine planes. The notion of translation generalized quadrangle is a local analogue of the more global ?Moufang Condition?, a topic of great interest, also due to the classification of all Moufang polygons. Attention is thus paid to recent results in that direction, but also many of the most important results in the general theory of generalized quadrangles that appeared since 1984 are treated.Translation Generalized Quadrangles is essentially self-contained, as the reader is only expected to be familiar with some basic facts on finite generalized quadrangles. Proofs that are either too long or too technical are left out, or just sketched. The three standard works on generalized quadrangles are (co-)authored by the writers of this book: ?Finite Generalized Quadrangles? (1984) by S E Payne and J A Thas, ?Generalized Polygons? (1998) by H Van Maldeghem, and ?Symmetry in Finite Generalized Quadrangles? (2004) by K Thas.
Moufang Polygons
This book gives the complete classification of Moufang polygons, starting from first principles. In particular, it may serve as an introduction to the various important algebraic concepts which arise in this classification including alternative division rings, quadratic Jordan division algebras of degree three, pseudo-quadratic forms, BN-pairs and norm splittings of quadratic forms. This book also contains a new proof of the classification of irreducible spherical buildings of rank at least three based on the observation that all the irreducible rank two residues of such a building are Moufang polygons. In an appendix, the connection between spherical buildings and algebraic groups is recalled.
