The Mathieu Groups PDF Download
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Author: A. A. Ivanov
Publisher: Cambridge University Press
ISBN: 1108637523
Category : Mathematics
Languages : en
Pages : 216
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Book Description
The Mathieu groups have many fascinating and unusual characteristics and have been studied at length since their discovery. This book provides a unique, geometric perspective on these groups. The amalgam method is explained and used to construct M24, enabling readers to learn the method through its application to a familiar example. The same method is then used to construct, among others, the octad graph, the Witt design and the Golay code. This book also provides a systematic account of 'small groups', and serves as a useful reference for the Mathieu groups. The material is presented in such a way that it guides the reader smoothly and intuitively through the process, leading to a deeper understanding of the topic.
Author: A. A. Ivanov
Publisher: Cambridge University Press
ISBN: 1108637523
Category : Mathematics
Languages : en
Pages : 216
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Book Description
The Mathieu groups have many fascinating and unusual characteristics and have been studied at length since their discovery. This book provides a unique, geometric perspective on these groups. The amalgam method is explained and used to construct M24, enabling readers to learn the method through its application to a familiar example. The same method is then used to construct, among others, the octad graph, the Witt design and the Golay code. This book also provides a systematic account of 'small groups', and serves as a useful reference for the Mathieu groups. The material is presented in such a way that it guides the reader smoothly and intuitively through the process, leading to a deeper understanding of the topic.
Author: Robert L. Jr. Griess
Publisher: Springer Science & Business Media
ISBN: 9783540627784
Category : Mathematics
Languages : en
Pages : 184
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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.
Author: Michael Aschbacher
Publisher: Cambridge University Press
ISBN: 9780521420495
Category : Mathematics
Languages : en
Pages : 336
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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.
Author: Mark Ronan
Publisher: Oxford University Press
ISBN: 0192807234
Category : Biography & Autobiography
Languages : en
Pages : 264
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Book Description
In an exciting, fast-paced historical narrative ranging across two centuries, Ronan takes readers on an exhilarating tour of this final mathematical quest to understand symmetry.
Author: John D. Dixon
Publisher: Springer Science & Business Media
ISBN: 1461207312
Category : Mathematics
Languages : en
Pages : 360
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Book Description
Following the basic ideas, standard constructions and important examples in the theory of permutation groups, the book goes on to develop the combinatorial and group theoretic structure of primitive groups leading to the proof of the pivotal ONan-Scott Theorem which links finite primitive groups with finite simple groups. Special topics covered include the Mathieu groups, multiply transitive groups, and recent work on the subgroups of the infinite symmetric groups. With its many exercises and detailed references to the current literature, this text can serve as an introduction to permutation groups in a course at the graduate or advanced undergraduate level, as well as for self-study.
Author: Joseph J. Rotman
Publisher: Springer Science & Business Media
ISBN: 1461245761
Category : Mathematics
Languages : en
Pages : 447
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Book Description
A clear exposition, with exercises, of the basic ideas of algebraic topology. Suitable for a two-semester course at the beginning graduate level, it assumes a knowledge of point set topology and basic algebra. Although categories and functors are introduced early in the text, excessive generality is avoided, and the author explains the geometric or analytic origins of abstract concepts as they are introduced.
Author: Robert Curtis
Publisher: Cambridge University Press
ISBN: 052185721X
Category : Mathematics
Languages : en
Pages : 333
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Book Description
Comprehensive text which develops the notion of symmetric generation and applies the technique to sporadic simple groups.
Author: Helmut Wielandt
Publisher: Academic Press
ISBN: 1483258297
Category : Mathematics
Languages : en
Pages : 125
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Book Description
Finite Permutation Groups provides an introduction to the basic facts of both the theory of abstract finite groups and the theory of permutation groups. This book deals with older theorems on multiply transitive groups as well as on simply transitive groups. Organized into five chapters, this book begins with an overview of the fundamental concepts of notation and Frobenius group. This text then discusses the modifications of multiple transitivity and can be used to deduce an improved form of the classical theorem. Other chapters consider the concept of simply transitive permutation groups. This book discusses as well permutation groups in the framework of representation theory. The final chapter deals with Frobenius' theory of group characters. This book is a valuable resource for engineers, mathematicians, and research workers. Graduate students and readers who are interested in finite permutation groups will also find this book useful.
Author: Philip J. Greenberg
Publisher:
ISBN:
Category : Group theory
Languages : en
Pages : 200
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Book Description
Author: William S. Burnside
Publisher: Courier Corporation
ISBN: 0486159442
Category : Mathematics
Languages : en
Pages : 545
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Book Description
Classic 1911 edition covers many group-related properties, including an extensive treatment of permutation groups and groups of linear substitutions, along with graphic representation of groups, congruence groups, and special topics.
