Author: A. A. IvanovPublisher: Cambridge University Press
ISBN: 0521413621
Category : Mathematics
Languages : en
Pages : 434
Book Description
Important monograph on finite group theory.
Geometry of Sporadic Groups: Volume 1, Petersen and Tilde Geometries
Author: A. A. IvanovPublisher: Cambridge University Press
ISBN: 0521413621
Category : Mathematics
Languages : en
Pages : 434
Book Description
Important monograph on finite group theory.
Geometry of Sporadic Groups: Volume 2, Representations and Amalgams
Author: Aleksandr Anatolievich IvanovPublisher: Cambridge University Press
ISBN: 0521623499
Category : Mathematics
Languages : en
Pages : 306
Book Description
The second in a two-volume set, for researchers into finite groups, geometry and algebraic combinatorics.
Twelve Sporadic Groups
Author: Robert L. Jr. GriessPublisher: Springer Science & Business Media
ISBN: 9783540627784
Category : Mathematics
Languages : en
Pages : 184
Book Description
The 20 sporadics involved in the Monster, the largest sporadic group, constitute the Happy Family. This book is a leisurely and rigorous study of two of their three generations. The level is suitable for graduate students with little background in general finite group theory, established mathematicians and mathematical physicists.
Sporadic Groups
Author: Michael AschbacherPublisher: Cambridge University Press
ISBN: 9780521420495
Category : Mathematics
Languages : en
Pages : 336
Book Description
Sporadic Groups is the first step in a programme to provide a uniform, self-contained treatment of the foundational material on the sporadic finite simple groups. The classification of the finite simple groups is one of the premier achievements of modern mathematics. The classification demonstrates that each finite simple group is either a finite analogue of a simple Lie group or one of 26 pathological sporadic groups. Sporadic Groups provides for the first time a self-contained treatment of the foundations of the theory of sporadic groups accessible to mathematicians with a basic background in finite groups such as in the author's text Finite Group Theory. Introductory material useful for studying the sporadics, such as a discussion of large extraspecial 2-subgroups and Tits' coset geometries, opens the book. A construction of the Mathieu groups as the automorphism groups of Steiner systems follows. The Golay and Todd modules, and the 2-local geometry for M24 are discussed. This is followed by the standard construction of Conway of the Leech lattice and the Conway group. The Monster is constructed as the automorphism group of the Griess algebra using some of the best features of the approaches of Griess, Conway, and Tits, plus a few new wrinkles. Researchers in finite group theory will find this text invaluable. The subjects treated will interest combinatorists, number theorists, and conformal field theorists.
Classifying Spaces of Sporadic Groups
Author: David J. BensonPublisher: American Mathematical Soc.
ISBN: 0821844741
Category : Mathematics
Languages : en
Pages : 310
Book Description
For each of the 26 sporadic finite simple groups, the authors construct a 2-completed classifying space using a homotopy decomposition in terms of classifying spaces of suitable 2-local subgroups. This construction leads to an additive decomposition of the mod 2 group cohomology.
Groups, Combinatorics and Geometry
Author: Martin W. LiebeckPublisher: Cambridge University Press
ISBN: 0521406854
Category : Mathematics
Languages : en
Pages : 505
Book Description
This volume contains a collection of papers on the subject of the classification of finite simple groups.
The Classification of the Finite Simple Groups, Number 3
Author: Daniel GorensteinPublisher: American Mathematical Soc.
ISBN: 9780821803912
Category : Finite simple groups
Languages : en
Pages : 446
Book Description
Examines the internal structure of the finite simple groups of Lie type, the finite alternating groups, and 26 sporadic finite simple groups, as well as their analogues. Emphasis is on the structure of local subgroups and their relationships with one another, rather than development of an abstract theory of simple groups. A foundation is laid for the development of specific properties of K-groups to be used in the inductive proof of the classification theorem. Highlights include statements and proofs of the Breol-Tits and Curtis-Tits theorems, and material on centralizers of semisimple involutions in groups of Lie type. For graduate students and research mathematicians. Annotation copyrighted by Book News, Inc., Portland, OR
Finite Simple Groups: Thirty Years of the Atlas and Beyond
Author: Manjul BhargavaPublisher: American Mathematical Soc.
ISBN: 1470436787
Category : Biography & Autobiography
Languages : en
Pages : 242
Book Description
Classification of Finite Simple Groups, one of the most monumental accomplishments of modern mathematics, was announced in 1983 with the proof completed in 2004. Since then, it has opened up a new and powerful strategy to approach and resolve many previously inaccessible problems in group theory, number theory, combinatorics, coding theory, algebraic geometry, and other areas of mathematics. This strategy crucially utilizes various information about finite simple groups, part of which is catalogued in the Atlas of Finite Groups (John H. Conway et al.), and in An Atlas of Brauer Characters (Christoph Jansen et al.). It is impossible to overestimate the roles of the Atlases and the related computer algebra systems in the everyday life of researchers in many areas of contemporary mathematics. The main objective of the conference was to discuss numerous applications of the Atlases and to explore recent developments and future directions of research, with focus on the interaction between computation and theory and applications to number theory and algebraic geometry. The papers in this volume are based on talks given at the conference. They present a comprehensive survey on current research in all of these fields.
Theory of Finite Simple Groups
Author: Gerhard MichlerPublisher: Cambridge University Press
ISBN: 0521866251
Category : Mathematics
Languages : en
Pages : 638
Book Description
The first representation theoretic and algorithmic approach to the theory of abstract finite simple groups.
The Geometry of Heisenberg Groups
Author: Ernst BinzPublisher: American Mathematical Soc.
ISBN: 0821844954
Category : Mathematics
Languages : en
Pages : 321
Book Description
"The three-dimensional Heisenberg group, being a quite simple non-commutative Lie group, appears prominently in various applications of mathematics. The goal of this book is to present basic geometric and algebraic properties of the Heisenberg group and its relation to other important mathematical structures (the skew field of quaternions, symplectic structures, and representations) and to describe some of its applications. In particular, the authors address such subjects as signal analysis and processing, geometric optics, and quantization. In each case, the authors present necessary details of the applied topic being considered." "This book manages to encompass a large variety of topics being easily accessible in its fundamentals. It can be useful to students and researchers working in mathematics and in applied mathematics."--BOOK JACKET.