Applying The Classification Of Finite Simple Groups
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Applying The Classification Of Finite Simple Groups
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Author : Stephen D. Smith
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-04-30
Applying The Classification Of Finite Simple Groups written by Stephen D. Smith and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-30 with Mathematics categories.
Classification of Finite Simple Groups (CFSG) is a major project involving work by hundreds of researchers. The work was largely completed by about 1983, although final publication of the “quasithin” part was delayed until 2004. Since the 1980s, CFSG has had a huge influence on work in finite group theory and in many adjacent fields of mathematics. This book attempts to survey and sample a number of such topics from the very large and increasingly active research area of applications of CFSG. The book is based on the author's lectures at the September 2015 Venice Summer School on Finite Groups. With about 50 exercises from original lectures, it can serve as a second-year graduate course for students who have had first-year graduate algebra. It may be of particular interest to students looking for a dissertation topic around group theory. It can also be useful as an introduction and basic reference; in addition, it indicates fuller citations to the appropriate literature for readers who wish to go on to more detailed sources.
Proceedings Of The Rutgers Group Theory Year 1983 1984
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Author : Michael Aschbacher
language : en
Publisher: Cambridge University Press
Release Date : 1984-12-28
Proceedings Of The Rutgers Group Theory Year 1983 1984 written by Michael Aschbacher and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-12-28 with Mathematics categories.
"With the classification of finite groups, an era of research in the subject ended. Some of the key figures in the classification program organized a research year at Rutgers University to analyze future directions of research in group theory. This volume is a record of the research year"- verso
Applied Differential Geometry
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Author : Vladimir G. Ivancevic
language : en
Publisher: World Scientific
Release Date : 2007
Applied Differential Geometry written by Vladimir G. Ivancevic and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This graduate-level monographic textbook treats applied differential geometry from a modern scientific perspective. Co-authored by the originator of the world's leading human motion simulator ? ?Human Biodynamics Engine?, a complex, 264-DOF bio-mechanical system, modeled by differential-geometric tools ? this is the first book that combines modern differential geometry with a wide spectrum of applications, from modern mechanics and physics, via nonlinear control, to biology and human sciences. The book is designed for a two-semester course, which gives mathematicians a variety of applications for their theory and physicists, as well as other scientists and engineers, a strong theory underlying their models.
Applied Abstract Algebra
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Author : Rudolf Lidl
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Applied Abstract Algebra written by Rudolf Lidl and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
Accessible to junior and senior undergraduate students, this survey contains many examples, solved exercises, sets of problems, and parts of abstract algebra of use in many other areas of discrete mathematics. Although this is a mathematics book, the authors have made great efforts to address the needs of users employing the techniques discussed. Fully worked out computational examples are backed by more than 500 exercises throughout the 40 sections. This new edition includes a new chapter on cryptology, and an enlarged chapter on applications of groups, while an extensive chapter has been added to survey other applications not included in the first edition. The book assumes knowledge of the material covered in a course on linear algebra and, preferably, a first course in (abstract) algebra covering the basics of groups, rings, and fields.
Representations Of Algebras
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Author : Vlastimil Dlab
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Representations Of Algebras written by Vlastimil Dlab and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
The Sixth International Conference on Representations of Algebras was held at Carleton University in Ottawa, Canada, in August 1992. This refereed volume contains papers presented at the conference, as well as a number of papers submitted after the conference. Describing developments at the forefront of the field, this book will be of interest to algebraists working in the field of representation theory.
Field Arithmetic
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Author : Michael D. Fried
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-04-09
Field Arithmetic written by Michael D. Fried and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-09 with Mathematics categories.
Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements. Progress from the first edition starts by characterizing the finite-field like P(seudo)A(lgebraically)C(losed) fields. We once believed PAC fields were rare. Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of the rationals PAC; and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)? The third edition improves the second edition in two ways: First it removes many typos and mathematical inaccuracies that occur in the second edition (in particular in the references). Secondly, the third edition reports on five open problems (out of thirtyfour open problems of the second edition) that have been partially or fully solved since that edition appeared in 2005.
Rank 2 Amalgams And Fusion Systems
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Author : Martin van Beek
language : en
Publisher: Springer Nature
Release Date : 2024-04-19
Rank 2 Amalgams And Fusion Systems written by Martin van Beek and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-19 with Mathematics categories.
This monograph provides a comprehensive treatment of the classification of small fusion systems, that is, fusion systems with few essential subgroups. It demonstrates a broad range of techniques from local group theory and fusion systems, several of which can be applied in more general settings. Addressing research problems that have not been treated in the past, it is the first text to explicitly use the amalgam method in this context. Fusion systems offer an enticing way to unify various p-local methods employed in group theory, representation theory and homotopy theory; but as abstract constructions they are still somewhat mysterious. This book paves the way to a broad and systematic study of these categories by applying the amalgam method, thus modernizing a methodology widely used to understand the local structure of finite groups. With this comes an introduction to several vital techniques in local group theory, a generous survey of the structure and modular representation theory of some important families of finite groups, and a demonstration of the value of combinatorial methods in finite group theory and fusion systems. Primarily aimed at researchers active in fusion systems and group amalgams, the book will also be of interest to anyone working with finite groups and their modular representations, group actions on trees, or classifying spaces. The inclusion of preliminary chapters outlining the theoretical prerequisites make it ideal for a short lecture course or as a reading group text for early career researchers and graduate students.
Hopf Algebras And Tensor Categories
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Author : Nicolás Andruskiewitsch
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-02-21
Hopf Algebras And Tensor Categories written by Nicolás Andruskiewitsch and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-21 with Mathematics categories.
This volume contains the proceedings of the Conference on Hopf Algebras and Tensor Categories, held July 4-8, 2011, at the University of Almeria, Almeria, Spain. The articles in this volume cover a wide variety of topics related to the theory of Hopf algebras and its connections to other areas of mathematics. In particular, this volume contains a survey covering aspects of the classification of fusion categories using Morita equivalence methods, a long comprehensive introduction to Hopf algebras in the category of species, and a summary of the status to date of the classification of Hopf algebras of dimensions up to 100. Among other topics discussed in this volume are a study of normalized class sum and generalized character table for semisimple Hopf algebras, a contribution to the classification program of finite dimensional pointed Hopf algebras, relations to the conjecture of De Concini, Kac, and Procesi on representations of quantum groups at roots of unity, a categorical approach to the Drinfeld double of a braided Hopf algebra via Hopf monads, an overview of Hom-Hopf algebras, and several discussions on the crossed product construction in different settings.
Handbook Of Combinatorics Volume 1
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Author : Ronald L. Graham
language : en
Publisher: Elsevier
Release Date : 1995-12-11
Handbook Of Combinatorics Volume 1 written by Ronald L. Graham and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-12-11 with Business & Economics categories.
Handbook of Combinatorics, Volume 1 focuses on basic methods, paradigms, results, issues, and trends across the broad spectrum of combinatorics. The selection first elaborates on the basic graph theory, connectivity and network flows, and matchings and extensions. Discussions focus on stable sets and claw free graphs, nonbipartite matching, multicommodity flows and disjoint paths, minimum cost circulations and flows, special proof techniques for paths and circuits, and Hamilton paths and circuits in digraphs. The manuscript then examines coloring, stable sets, and perfect graphs and embeddings and minors. The book takes a look at random graphs, hypergraphs, partially ordered sets, and matroids. Topics include geometric lattices, structural properties, linear extensions and correlation, dimension and posets of bounded degree, hypergraphs and set systems, stability, transversals, and matchings, and phase transition. The manuscript also reviews the combinatorial number theory, point lattices, convex polytopes and related complexes, and extremal problems in combinatorial geometry. The selection is a valuable reference for researchers interested in combinatorics.
Simplicity Theory
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Author : Byunghan Kim
language : en
Publisher: Oxford Logic Guides
Release Date : 2014
Simplicity Theory written by Byunghan Kim and has been published by Oxford Logic Guides this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Mathematics categories.
An up-to-date account of the current techniques and results in Simplicity Theory, which has been a focus of research in model theory for the last decade. Suitable for logicians, mathematicians and graduate students working on model theory.