Groups Combinatorics & Geometry

Groups Combinatorics & Geometry
Author: A. A. Ivanov
Publisher: World Scientific
Total Pages: 350
Release: 2003
Genre: Mathematics
ISBN: 9789812564481

Over the past 20 years, the theory of groups in particular simplegroups, finite and algebraic has influenced a number of diverseareas of mathematics. Such areas include topics where groups have beentraditionally applied, such as algebraic combinatorics, finitegeometries, Galois theory and permutation groups, as well as severalmore recent developments.

Groups and Geometries

Groups and Geometries
Author: Lino Di Martino
Publisher: Birkhäuser
Total Pages: 267
Release: 2013-12-01
Genre: Mathematics
ISBN: 3034888198

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 collection of themes for a broad range of algebraists and geometers. Among those themes, represented within the conference or these Proceedings, are aspects of the following: 1. the classification of finite simple groups, 2. the structure and properties of groups of Lie type over finite and algebraically closed fields of finite characteristic, 3. buildings, and the geometry of projective and polar spaces, and 4. geometries of sporadic simple groups. We are grateful to the authors for their efforts in providing us with manuscripts in LaTeX. Barbara Priwitzer and Thomas Hintermann, Mathematics Editors of Birkhauser, have been very helpful and supportive throughout the preparation of this volume.

Groups, Combinatorics and Geometry

Groups, Combinatorics and Geometry
Author: Martin W. Liebeck
Publisher: Cambridge University Press
Total Pages: 505
Release: 1992-09-10
Genre: Mathematics
ISBN: 0521406854

This volume contains a collection of papers on the subject of the classification of finite simple groups.

The Mathieu Groups

The Mathieu Groups
Author: A. A. Ivanov
Publisher: Cambridge University Press
Total Pages: 185
Release: 2018-06-21
Genre: Mathematics
ISBN: 1108429785

The Mathieu Groups are presented in the context of finite geometry and the theory of group amalgams.

Handbook of Combinatorics

Handbook of Combinatorics
Author: R.L. Graham
Publisher: Elsevier
Total Pages: 2404
Release: 1995-12-11
Genre: Computers
ISBN: 008093384X

Handbook of Combinatorics

The Classification of the Finite Simple Groups, Number 2

The Classification of the Finite Simple Groups, Number 2
Author: Daniel Gorenstein
Publisher: American Mathematical Soc.
Total Pages: 246
Release: 1994
Genre: Mathematics
ISBN: 9780821803905

The second volume of a series devoted to reorganizing and simplifying proof of the classification of the finite simple groups. In a single chapter, it lays the groundwork for the forthcoming analysis of finite simple groups, beginning with the theory of components, layers, and the generalized Fitting subgroup, which has been developed largely since Gorenstein's basic 1968 text and is now central to understanding the structure of finite groups. Suitable as an auxiliary text for a graduate course in group theory. Member prices are $35 for individual and $47 for institutions. Annotation copyright by Book News, Inc., Portland, OR

The Classification of Quasithin Groups

The Classification of Quasithin Groups
Author: Michael Aschbacher
Publisher: American Mathematical Soc.
Total Pages: 496
Release: 2004
Genre: Mathematics
ISBN: 082183410X

The first of two volumes, this text offers results that are used in the proof of the main theoremthat lies behind quasithin groups, an class of finite simple groups. Some results are gathered from existing mathematical literature, but many are proven for the first time.

Investigations in Algebraic Theory of Combinatorial Objects

Investigations in Algebraic Theory of Combinatorial Objects
Author: I.A. Faradzev
Publisher: Springer Science & Business Media
Total Pages: 513
Release: 2013-06-29
Genre: Mathematics
ISBN: 9401719721

X Köchendorffer, L.A. Kalu:lnin and their students in the 50s and 60s. Nowadays the most deeply developed is the theory of binary invariant relations and their combinatorial approximations. These combinatorial approximations arose repeatedly during this century under various names (Hecke algebras, centralizer rings, association schemes, coherent configurations, cellular rings, etc.-see the first paper of the collection for details) andin various branches of mathematics, both pure and applied. One of these approximations, the theory of cellular rings (cellular algebras), was developed at the end of the 60s by B. Yu. Weisfeiler and A.A. Leman in the course of the first serious attempt to study the complexity of the graph isomorphism problem, one of the central problems in the modern theory of combinatorial algorithms. At roughly the same time G.M. Adelson-Velskir, V.L. Arlazarov, I.A. Faradtev and their colleagues had developed a rather efficient tool for the constructive enumeration of combinatorial objects based on the branch and bound method. By means of this tool a number of "sports-like" results were obtained. Some of these results are still unsurpassed.

Symplectic Amalgams

Symplectic Amalgams
Author: Christopher Parker
Publisher: Springer Science & Business Media
Total Pages: 362
Release: 2012-12-06
Genre: Mathematics
ISBN: 1447101650

The aim of this book is the classification of symplectic amalgams - structures which are intimately related to the finite simple groups. In all there sixteen infinite families of symplectic amalgams together with 62 more exotic examples. The classification touches on many important aspects of modern group theory: * p-local analysis * the amalgam method * representation theory over finite fields; and * properties of the finite simple groups. The account is for the most part self-contained and the wealth of detail makes this book an excellent introduction to these recent developments for graduate students, as well as a valuable resource and reference for specialists in the area.