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Author: Aleksandr Anatolievich Ivanov
Publisher: Cambridge University Press
ISBN: 0521623499
Category : Mathematics
Languages : en
Pages : 306
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Book Description
The second in a two-volume set, for researchers into finite groups, geometry and algebraic combinatorics.
Author: Aleksandr Anatolievich Ivanov
Publisher: Cambridge University Press
ISBN: 0521623499
Category : Mathematics
Languages : en
Pages : 306
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Book Description
The second in a two-volume set, for researchers into finite groups, geometry and algebraic combinatorics.
Author: A. A. Ivanov
Publisher: Cambridge University Press
ISBN: 0521413621
Category : Mathematics
Languages : en
Pages : 434
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Book Description
Important monograph on finite group theory.
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: David J. Benson
Publisher: American Mathematical Soc.
ISBN: 0821844741
Category : Mathematics
Languages : en
Pages : 310
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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.
Author: Aleksandr Anatolievich Ivanov
Publisher: Cambridge University Press
ISBN: 0521889944
Category : Mathematics
Languages : en
Pages : 267
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Book Description
A rigorous construction and uniqueness proof for the Monster group, detailing its relation to Majorana involutions.
Author: M. Lothaire
Publisher: Cambridge University Press
ISBN: 9780521848022
Category : Computers
Languages : en
Pages : 646
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Book Description
Publisher Description
Author: Robert Wilson
Publisher: Springer Science & Business Media
ISBN: 1848009887
Category : Mathematics
Languages : en
Pages : 310
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Book Description
Thisbookisintendedasanintroductiontoallthe?nitesimplegroups.During themonumentalstruggletoclassifythe?nitesimplegroups(andindeedsince), a huge amount of information about these groups has been accumulated. Conveyingthisinformationtothenextgenerationofstudentsandresearchers, not to mention those who might wish to apply this knowledge, has become a major challenge. With the publication of the two volumes by Aschbacher and Smith [12, 13] in 2004 we can reasonably regard the proof of the Classi?cation Theorem for Finite Simple Groups (usually abbreviated CFSG) as complete. Thus it is timely to attempt an overview of all the (non-abelian) ?nite simple groups in one volume. For expository purposes it is convenient to divide them into four basic types, namely the alternating, classical, exceptional and sporadic groups. The study of alternating groups soon develops into the theory of per- tation groups, which is well served by the classic text of Wielandt [170]and more modern treatments such as the comprehensive introduction by Dixon and Mortimer [53] and more specialised texts such as that of Cameron [19].
Author: R. J. McEliece
Publisher: Cambridge University Press
ISBN: 9780521831857
Category : Computers
Languages : en
Pages : 414
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Book Description
Student edition of the classic text in information and coding theory
Author: Stephen D. Smith
Publisher: American Mathematical Soc.
ISBN: 0821805010
Category : Mathematics
Languages : en
Pages : 378
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Book Description
This book is intended as an overview of a research area that combines geometries for groups (such as Tits buildings and generalizations), topological aspects of simplicial complexes from $p$-subgroups of a group (in the spirit of Brown, Quillen, and Webb), and combinatorics of partially ordered sets. The material is intended to serve as an advanced graduate-level text and partly as a general reference on the research area. The treatment offers optional tracks for the reader interested in buildings, geometries for sporadic simple groups, and $G$-equivariant equivalences and homology for subgroup complexes.
