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Contributions To The Theory Of Groups
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Book Synopsis Complexity and Randomness in Group Theory by : Frédérique Bassino
Download or read book Complexity and Randomness in Group Theory written by Frédérique Bassino and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-06-08 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows new directions in group theory motivated by computer science. It reflects the transition from geometric group theory to group theory of the 21st century that has strong connections to computer science. Now that geometric group theory is drifting further and further away from group theory to geometry, it is natural to look for new tools and new directions in group theory which are present.
Book Synopsis The Theory of Classes of Groups by : Guo Wenbin
Download or read book The Theory of Classes of Groups written by Guo Wenbin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the characteristics of modern algebra is the development of new tools and concepts for exploring classes of algebraic systems, whereas the research on individual algebraic systems (e. g. , groups, rings, Lie algebras, etc. ) continues along traditional lines. The early work on classes of alge bras was concerned with showing that one class X of algebraic systems is actually contained in another class F. Modern research into the theory of classes was initiated in the 1930's by Birkhoff's work [1] on general varieties of algebras, and Neumann's work [1] on varieties of groups. A. I. Mal'cev made fundamental contributions to this modern development. ln his re ports [1, 3] of 1963 and 1966 to The Fourth All-Union Mathematics Con ference and to another international mathematics congress, striking the ories of classes of algebraic systems were presented. These were later included in his book [5]. International interest in the theory of formations of finite groups was aroused, and rapidly heated up, during this time, thanks to the work of Gaschiitz [8] in 1963, and the work of Carter and Hawkes [1] in 1967. The major topics considered were saturated formations, Fitting classes, and Schunck classes. A class of groups is called a formation if it is closed with respect to homomorphic images and subdirect products. A formation is called saturated provided that G E F whenever Gjip(G) E F.
Book Synopsis The Genesis of the Abstract Group Concept by : Hans Wussing
Download or read book The Genesis of the Abstract Group Concept written by Hans Wussing and published by Courier Corporation. This book was released on 2007-01-01 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: "It is a pleasure to turn to Wussing's book, a sound presentation of history," declared the Bulletin of the American Mathematical Society. The author, Director of the Institute for the History of Medicine and Science at Leipzig University, traces the axiomatic formulation of the abstract notion of group. 1984 edition.
Book Synopsis Theory of Lie Groups by : Claude Chevalley
Download or read book Theory of Lie Groups written by Claude Chevalley and published by Princeton University Press. This book was released on 2000-01-10 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This famous book was the first treatise on Lie groups in which a modern point of view was adopted systematically, namely, that a continuous group can be regarded as a global object. To develop this idea to its fullest extent, Chevalley incorporated a broad range of topics, such as the covering spaces of topological spaces, analytic manifolds, integration of complete systems of differential equations on a manifold, and the calculus of exterior differential forms. The book opens with a short description of the classical groups: unitary groups, orthogonal groups, symplectic groups, etc. These special groups are then used to illustrate the general properties of Lie groups, which are considered later. The general notion of a Lie group is defined and correlated with the algebraic notion of a Lie algebra; the subgroups, factor groups, and homomorphisms of Lie groups are studied by making use of the Lie algebra. The last chapter is concerned with the theory of compact groups, culminating in Peter-Weyl's theorem on the existence of representations. Given a compact group, it is shown how one can construct algebraically the corresponding Lie group with complex parameters which appears in the form of a certain algebraic variety (associated algebraic group). This construction is intimately related to the proof of the generalization given by Tannaka of Pontrjagin's duality theorem for Abelian groups. The continued importance of Lie groups in mathematics and theoretical physics make this an indispensable volume for researchers in both fields.
Book Synopsis Groups at Work by : Marlene E. Turner
Download or read book Groups at Work written by Marlene E. Turner and published by Psychology Press. This book was released on 2014-04-04 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has two purposes. First, it is fundamentally about groups at work, both as they attempt to accomplish their goals and as they operate in organizational settings. Second, it draws together group researchers from social psychological and organizational studies. Each chapter focuses on a central issue regarding groups as they work and examines that issue by drawing from both social psychological and organizational research. Thus, this book centers on the convergence and divergence of these two fields.
Book Synopsis The History of Combinatorial Group Theory by : B. Chandler
Download or read book The History of Combinatorial Group Theory written by B. Chandler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the pervasive phenomena in the history of science is the development of independent disciplines from the solution or attempted solutions of problems in other areas of science. In the Twentieth Century, the creation of specialties witqin the sciences has accelerated to the point where a large number of scientists in any major branch of science cannot understand the work of a colleague in another subdiscipline of his own science. Despite this fragmentation, the development of techniques or solutions of problems in one area very often contribute fundamentally to solutions of problems in a seemingly unrelated field. Therefore, an examination of this phenomenon of the formation of independent disciplines within the sciences would contrib ute to the understanding of their evolution in modern times. We believe that in this context the history of combinatorial group theory in the late Nineteenth Century and the Twentieth Century can be used effectively as a case study. It is a reasonably well-defined independent specialty, and yet it is closely related to other mathematical disciplines. The fact that combinatorial group theory has, so far, not been influenced by the practical needs of science and technology makes it possible for us to use combinatorial group theory to exhibit the role of the intellectual aspects of the development of mathematics in a clearcut manner. There are other features of combinatorial group theory which appear to make it a reasona ble choice as the object of a historical study.
Book Synopsis Theory of Groups of Finite Order by : William S. Burnside
Download or read book Theory of Groups of Finite Order written by William S. Burnside and published by Courier Corporation. This book was released on 2013-02-20 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Finite Group Theory by : M. Aschbacher
Download or read book Finite Group Theory written by M. Aschbacher and published by Cambridge University Press. This book was released on 2000-06-26 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last 40 years the theory of finite groups has developed dramatically. The finite simple groups have been classified and are becoming better understood. Tools exist to reduce many questions about arbitrary finite groups to similar questions about simple groups. Since the classification there have been numerous applications of this theory in other branches of mathematics. Finite Group Theory develops the foundations of the theory of finite groups. It can serve as a text for a course on finite groups for students already exposed to a first course in algebra. It could supply the background necessary to begin reading journal articles in the field. For specialists it also provides a reference on the foundations of the subject. This second edition has been considerably improved with a completely rewritten Chapter 15 considering the 2-Signalizer Functor Theorem, and the addition of an appendix containing solutions to exercises.
Book Synopsis Topological Methods in Group Theory by : Ross Geoghegan
Download or read book Topological Methods in Group Theory written by Ross Geoghegan and published by Springer Science & Business Media. This book was released on 2007-12-17 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit.
Book Synopsis Group Theory in a Nutshell for Physicists by : A. Zee
Download or read book Group Theory in a Nutshell for Physicists written by A. Zee and published by Princeton University Press. This book was released on 2016-03-29 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise, modern textbook on group theory written especially for physicists Although group theory is a mathematical subject, it is indispensable to many areas of modern theoretical physics, from atomic physics to condensed matter physics, particle physics to string theory. In particular, it is essential for an understanding of the fundamental forces. Yet until now, what has been missing is a modern, accessible, and self-contained textbook on the subject written especially for physicists. Group Theory in a Nutshell for Physicists fills this gap, providing a user-friendly and classroom-tested text that focuses on those aspects of group theory physicists most need to know. From the basic intuitive notion of a group, A. Zee takes readers all the way up to how theories based on gauge groups could unify three of the four fundamental forces. He also includes a concise review of the linear algebra needed for group theory, making the book ideal for self-study. Provides physicists with a modern and accessible introduction to group theory Covers applications to various areas of physics, including field theory, particle physics, relativity, and much more Topics include finite group and character tables; real, pseudoreal, and complex representations; Weyl, Dirac, and Majorana equations; the expanding universe and group theory; grand unification; and much more The essential textbook for students and an invaluable resource for researchers Features a brief, self-contained treatment of linear algebra An online illustration package is available to professors Solutions manual (available only to professors)
Book Synopsis The Handbook of Group Communication Theory and Research by : Lawrence R. Frey
Download or read book The Handbook of Group Communication Theory and Research written by Lawrence R. Frey and published by SAGE. This book was released on 1999-07-08 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: Documents and synthesizes work done in group communication scholarship's 50-year history, presenting an overview of group communication study from its beginnings in pedagogy to its status as a mature discipline with a variety of theoretical positions and methodological practices. Material is divided
Book Synopsis Group Theory by : Predrag Cvitanović
Download or read book Group Theory written by Predrag Cvitanović and published by Princeton University Press. This book was released on 2008-07-01 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: If classical Lie groups preserve bilinear vector norms, what Lie groups preserve trilinear, quadrilinear, and higher order invariants? Answering this question from a fresh and original perspective, Predrag Cvitanovic takes the reader on the amazing, four-thousand-diagram journey through the theory of Lie groups. This book is the first to systematically develop, explain, and apply diagrammatic projection operators to construct all semi-simple Lie algebras, both classical and exceptional. The invariant tensors are presented in a somewhat unconventional, but in recent years widely used, "birdtracks" notation inspired by the Feynman diagrams of quantum field theory. Notably, invariant tensor diagrams replace algebraic reasoning in carrying out all group-theoretic computations. The diagrammatic approach is particularly effective in evaluating complicated coefficients and group weights, and revealing symmetries hidden by conventional algebraic or index notations. The book covers most topics needed in applications from this new perspective: permutations, Young projection operators, spinorial representations, Casimir operators, and Dynkin indices. Beyond this well-traveled territory, more exotic vistas open up, such as "negative dimensional" relations between various groups and their representations. The most intriguing result of classifying primitive invariants is the emergence of all exceptional Lie groups in a single family, and the attendant pattern of exceptional and classical Lie groups, the so-called Magic Triangle. Written in a lively and personable style, the book is aimed at researchers and graduate students in theoretical physics and mathematics.
Book Synopsis Contributions to the Theory of Games (AM-28), Volume II by : Harold William Kuhn
Download or read book Contributions to the Theory of Games (AM-28), Volume II written by Harold William Kuhn and published by Princeton University Press. This book was released on 2016-03-02 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: These two new collections, numbers 28 and 29 respectively in the Annals of Mathematics Studies, continue the high standard set by the earlier Annals Studies 20 and 24 by bringing together important contributions to the theories of games and of nonlinear differential equations.
Book Synopsis The Theory of Groups by : Marshall Hall Jr.
Download or read book The Theory of Groups written by Marshall Hall Jr. and published by . This book was released on 2012-06-01 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Combinatorial Group Theory by : Roger C. Lyndon
Download or read book Combinatorial Group Theory written by Roger C. Lyndon and published by Springer. This book was released on 2015-03-12 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This book [...] defines the boundaries of the subject now called combinatorial group theory. [...] it is a considerable achievement to have concentrated a survey of the subject into 339 pages. [...] a valuable and welcome addition to the literature, containing many results not previously available in a book. It will undoubtedly become a standard reference." Mathematical Reviews
Book Synopsis Subgroup Growth by : Alexander Lubotzky
Download or read book Subgroup Growth written by Alexander Lubotzky and published by Birkhäuser. This book was released on 2012-12-06 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2001. Subgroup growth studies the distribution of subgroups of finite index in a group as a function of the index. In the last two decades this topic has developed into one of the most active areas of research in infinite group theory; this book is a systematic and comprehensive account of the substantial theory which has emerged. As well as determining the range of possible 'growth types', for finitely generated groups in general and for groups in particular classes such as linear groups, a main focus of the book is on the tight connection between the subgroup growth of a group and its algebraic structure. A wide range of mathematical disciplines play a significant role in this work: as well as various aspects of infinite group theory, these include finite simple groups and permutation groups, profinite groups, arithmetic groups and Strong Approximation, algebraic and analytic number theory, probability, and p-adic model theory. Relevant aspects of such topics are explained in self-contained 'windows'.
Book Synopsis Richard Brauer - Collected Papers by : Richard Brauer
Download or read book Richard Brauer - Collected Papers written by Richard Brauer and published by MIT Press (MA). This book was released on 2003-02-01 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: Richard Brauer (1901-1977) was one of the leading algebraists of this century. Although he contributed to a number of mathematical fields, Brauer devoted the major share of his efforts to the study of finite groups, a subject of considerable abstract interest and one that underlies many of the more recent advances in combinatorics and finite geometries.
