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Group Theoretic Cryptography (Chapman & Hall/CRC Cryptography and Network Security Series)
by Maria Isabel Gonzalez Vasco Rainer SteinwandtGroup theory appears to be a promising source of hard computational problems for deploying new cryptographic constructions. This reference focuses on the specifics of using groups, including in particular non-Abelian groups, in the field of cryptography. It provides an introduction to cryptography with emphasis on the group theoretic perspective, making it one of the first books to use this approach. The authors provide the needed cryptographic and group theoretic concepts, full proofs of essential theorems, and formal security evaluations of the cryptographic schemes presented. They also provide references for further reading and exercises at the end of each chapter.
Group Theoretical Methods in Physics. Volume II: Proceedings of the Third Yurmala Seminar, Yurmala, USSR, 22-24 May 1985
by M. A. Markov V. I. Man'Ko V. V. DodonovThese Proceedings cover various topics in modern physics in which group theoretical methods can be applied effectively. The two volumes, containing over 100 papers, cover such areas as representation theory, the theory and applications of dynamical symmetries and coherent states, symmetries in atomic, molecular, nuclear and elementary particle physics, field theory including gauge theories, supersymmetry and supergravity, general relativity and cosmology, the theory of space groups and its applications to solid state physics and phase transitions, the problems of quantum and classical mechanics and paraxial optics, and the theory of nonlinear equations and solitons.
Group Theoretical Methods in Physics: Proceedings of the XXV International Colloqium on Group Theoretical Methods in Physics, Cocoyoc, Mexico, 2-6 August, 2004 (Institute of Physics Conference Series)
by George S. Pogosyan, Luis Edgar Vicent and Kurt Bernardo WolfThis book discusses group theoretical methods and their applications in physics, chemistry, and biology. It covers traditional subjects including Lie group and representation theory, special functions, foundations of quantum mechanics, and elementary particle, nuclear, atomic, and molecular physics. More recent areas discussed are supersymmetry, superstrings and quantum gravity, integrability, nonlinear systems and quantum chaos, semigroups, time asymmetry and resonances, condensed matter, and statistical physics. Topics such as linear and nonlinear optics, quantum computing, discrete systems, and signal analysis have only in the last few years become part of the group theorists' turf.
Group Theory
by Pierre RamondGroup theory has long been an important computational tool for physicists, but, with the advent of the Standard Model, it has become a powerful conceptual tool as well. This book introduces physicists to many of the fascinating mathematical aspects of group theory, and mathematicians to its physics applications. Designed for advanced undergraduate and graduate students, this book gives a comprehensive overview of the main aspects of both finite and continuous group theory, with an emphasis on applications to fundamental physics. Finite groups are extensively discussed, highlighting their irreducible representations and invariants. Lie algebras, and to a lesser extent Kac-Moody algebras, are treated in detail, including Dynkin diagrams. Special emphasis is given to their representations and embeddings. The group theory underlying the Standard Model is discussed, along with its importance in model building. Applications of group theory to the classification of elementary particles are treated in detail.
Group Theory (Dover Books on Mathematics)
by W. R. ScottWell-organized and clearly written, this undergraduate-level text covers most of the standard basic theorems in group theory, providing proofs of the basic theorems of both finite and infinite groups and developing as much of their superstructure as space permits. Contents include: Isomorphism Theorems, Direct Sums, p-Groups and p-Subgroups, Free Groups and Free Products, Permutation Groups, Transformations and Subgroups, Abelian Groups, Supersolvable Groups, Extensions, Representations, and more. The concluding chapters also cover a wide variety of further theorems, some not previously published in book form, including infinite symmetric and alternating groups, products of subgroups, the multiplicative group of a division ring, and FC groups.Over 500 exercises in varying degrees of difficulty enable students to test their grasp of the material, which is largely self-contained (except for later chapters which presuppose some knowledge of linear algebra, polynomials, algebraic integers, and elementary number theory). Also included are a bibliography, index, and an index of notation. Ideal as a text or for reference, this inexpensive paperbound edition of Group Theory offers mathematics students a lucid, highly useful introduction to an increasingly vital mathematical discipline. It will be welcomed by anyone in search of a cogent, thorough presentation that lends itself equally well to self-study or regular course work.
Group Theory I Essentials
by Emil MilewskiREA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Group Theory I includes sets and mapping, groupoids and semi-groups, groups, isomorphisms and homomorphisms, cyclic groups, the Sylow theorems, and finite p-groups.
Group Theory for High Energy Physicists
by Mohammad Saleem Muhammad RafiqueAlthough group theory has played a significant role in the development of various disciplines of physics, there are few recent books that start from the beginning and then build on to consider applications of group theory from the point of view of high energy physicists. Group Theory for High Energy Physicists fills that role. It presents groups, e
Group Theory in Particle, Nuclear, and Hadron Physics
by Syed Afsar AbbasThis user-friendly book on group theory introduces topics in as simple a manner as possible and then gradually develops those topics into more advanced ones, eventually building up to the current state-of-the-art. By using simple examples from physics and mathematics, the advanced topics become logical extensions of ideas already introduced. In addition to being used as a textbook, this book would also be useful as a reference guide for graduates and researchers in particle, nuclear and hadron physics.
Group Theory in Physics: An Introduction with a Focus on Solid State Physics (Undergraduate Lecture Notes in Physics)
by Jörg BünemannThis textbook provides a didactic introduction to the topic of group theory in physics, with a special focus on solid state physics issues. The book is useful for students who encounter such problems in their first scientific work (in theory or experiment). In addition to the basic introduction to group theory and representation theory, the book deals with point groups, double point groups, and space groups, which are essential in solid state physics. As an example for systems with space group symmetry, electrons in periodic potentials are discussed. Furthermore, there are chapters on material tensors and the Wigner Eckart theorem for the evaluation of matrix elements. The latter is especially interesting for students dealing with spectroscopic problems. The content is accompanied by a series of exercises and examples. A set of solutions can be found in the appendix.
Group Theory in the Bedroom, and Other Mathematical Diversions
by Brian HayesAn Award-Winning Essayist Plies His CraftBrian Hayes is one of the most accomplished essayists active today—a claim supported not only by his prolific and continuing high-quality output but also by such honors as the National Magazine Award for his commemorative Y2K essay titled "Clock of Ages," published in the November/December 1999 issue of The Sciences magazine. (The also-rans that year included Tom Wolfe, Verlyn Klinkenborg, and Oliver Sacks.) Hayes's work in this genre has also appeared in such anthologies as The BestAmerican Magazine Writing, The Best American Science and NatureWriting, and The Norton Reader. Here he offers us a selection of his most memorable and accessible pieces—including "Clock of Ages"—embellishing them with an overall, scene-setting preface, reconfigured illustrations, and a refreshingly self-critical "Afterthoughts" section appended to each essay.
Group-Theoretic Methods in Mechanics and Applied Mathematics
by D.M. KlimovGroup analysis of differential equations has applications to various problems in nonlinear mechanics and physics. Group-Theoretic Methods in Mechanics and Applied Mathematics systematizes the group analysis of the main postulates of classical and relativistic mechanics. Exact solutions are given for the following equations: dynamics of rigid body, heat transfer, wave, hydrodynamics, Thomas-Fermi, and more. The author pays particular attention to the application of group analysis to developing asymptotic methods for problems with small parameters. This book is designed for a broad audience of scientists, engineers, and students in the fields of applied mathematics, mechanics and physics.
Groupes algébriques semi-simples en dimension cohomologique ≤2: Semisimple algebraic groups in cohomological dimension ≤2 (Lecture Notes in Mathematics #2238)
by Philippe GilleLa théorie des groupes algébriques sur un corps arbitraire est l’une des branches les plus merveilleuses des mathématiques modernes. Cette monographie porte sur les groupes algébriques semi-simples définis sur un corps k de dimension cohomologique séparable ≤2 et la cohomologie galoisienne d’iceux. La question ouverte la plus importante est la conjecture II de Serre (1962) qui prédit l’annulation de la cohomologie galoisienne d’un groupe semi-simple simplement connexe.Utilisant principalement des techniques de groupes algébriques, on couvre tous les cas connus de la conjecture: les cas classiques (dus à Bayer-Fluckiger and Parimala) ainsi que les avancées sur les cas exceptionnels restants (par exemple de type E8). Ceci s’applique à la classification des groupes semi-simples. The theory of algebraic groups over arbitrary fields is one of the most beautiful branches of modern mathematics. This monograph deals with semisimple algebraic groups over a general field k of separable cohomological dimension ^ to Bayer-Fluckiger and Parimala), and some perspectives are given on the remaining exceptional cases (e.g., G of type E8). Applications to the classification of semisimple k-groups are presented.
Groupoid Metrization Theory
by Marius Mitrea Sylvie Monniaux Dorina Mitrea Irina MitreaThe topics in this research monograph are at the interface of several areas of mathematics such as harmonic analysis, functional analysis, analysis on spaces of homogeneous type, topology, and quasi-metric geometry. The presentation is self-contained with complete, detailed proofs, and a large number of examples and counterexamples are provided. Unique features of Metrization Theory for Groupoids: With Applications to Analysis on Quasi-Metric Spaces and Functional Analysis include: * treatment of metrization from a wide, interdisciplinary perspective, with accompanying applications ranging across diverse fields; * coverage of topics applicable to a variety of scientific areas within pure mathematics; * useful techniques and extensive reference material; * includes sharp results in the field of metrization. Professional mathematicians with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. At the same time, the monograph is accessible and will be of use to advanced graduate students and to scientifically trained readers with an interest in the interplay among topology and metric properties and/or functional analysis and metric properties. * coverage of topics applicable to a variety of scientific areas within pure mathematics; * useful techniques and extensive reference material; * includes sharp results in the field of metrization. Professional mathematicians with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. At the same time, the monograph is accessible and will be of use to advanced graduate students and to scientifically trained readers with an interest in the interplay among topology and metric properties and/or functional analysis and metric properties. * useful techniques and extensive reference material; * includes sharp results in the field of metrization. Professional mathematicians with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. At the same time, the monograph is accessible and will be of use to advanced graduate students and to scientifically trained readers with an interest in the interplay among topology and metric properties and/or functional analysis and metric properties. * includes sharp results in the field of metrization. Professional mathematicians with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. At the same time, the monograph is accessible and will be of use to advanced graduate students and to scientifically trained readers with an interest in the interplay among topology and metric properties and/or functional analysis and metric properties. Professional mathematicians with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. At the same time, the monograph is accessible and will be of use to advanced graduate students and to scientifically trained readers with an interest in the interplay among topology and metric properties and/or functional analysis and metric properties.
Groups
by Antonio MachìGroups are a means of classification, via the group action on a set, but also the object of a classification. How many groups of a given type are there, and how can they be described? Hölder's program for attacking this problem in the case of finite groups is a sort of leitmotiv throughout the text. Infinite groups are also considered, with particular attention to logical and decision problems. Abelian, nilpotent and solvable groups are studied both in the finite and infinite case. Permutation groups and are treated in detail; their relationship with Galois theory is often taken into account. The last two chapters deal with the representation theory of finite group and the cohomology theory of groups; the latter with special emphasis on the extension problem. The sections are followed by exercises; hints to the solution are given, and for most of them a complete solution is provided.
Groups St Andrews 2017 in Birmingham (London Mathematical Society Lecture Note Series #455)
by C. M. Campbell M. R. Quick E. F. Robertson C. W. Parker C. M. Roney-DougalEvery four years leading researchers gather to survey the latest developments in all aspects of group theory. Initially held in St Andrews, these meetings have become the premier forum for group theory across the whole of the UK. Since 1981, the proceedings of 'Groups St Andrews' have provided a regular snapshot of the state-of-the-art in group theory and helped to shape the direction of research in the field. This volume contains papers from the 2017 meeting held in Birmingham. It includes expository articles from the invited speakers, and further surveys contributed by the participants. Topics include: generation of finite simple groups, block theory, fusion systems, algebraic groups, one-relator groups, geometric group theory, and Beauville groups.
Groups and Characters
by Victor E HillGroup representation theory is both elegant and practical, with important applications to quantum mechanics, spectroscopy, crystallography, and other fields in the physical sciences. This book offers an easy-to-follow introduction to the theory of groups and of group characters. Designed as a rapid survey of the subject, it emphasizes examples and applications of the theorems, and avoids many of the longer and more difficult proofs. The text includes sections that provide the mathematical basis for some of the applications of group theory. It also offers numerous exercises, some stressing computation of concrete examples, others stressing development of the theory.
Groups of Exceptional Type, Coxeter Groups and Related Geometries
by N.S. Narasimha SastryThe book deals with fundamental structural aspects of algebraic and simple groups, Coxeter groups and the related geometries and buildings. All contributing authors are very active researchers in the topics related to the theme of the book. Some of the articles provide the latest developments in the subject; some provide an overview of the current status of some important problems in this area; some survey an area highlighting the current developments; and some provide an exposition of an area to collect problems and conjectures. It is hoped that these articles would be helpful to a beginner to start independent research on any of these topics, as well as to an expert to know some of the latest developments or to consider some problems for investigation.
Groups, Graphs and Random Walks (London Mathematical Society Lecture Note Series #436)
by Tullio Ceccherini-Silberstein Maura Salvatori Ecaterina Sava-HussAn accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schrdinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research activities will undoubtedly stem.
Groups, Invariants, Integrals, and Mathematical Physics: The Wisła 20-21 Winter School and Workshop (Tutorials, Schools, and Workshops in the Mathematical Sciences)
by Maria Ulan Stanislav HronekThis volume presents lectures given at the Wisła 20-21 Winter School and Workshop: Groups, Invariants, Integrals, and Mathematical Physics, organized by the Baltic Institute of Mathematics. The lectures were dedicated to differential invariants – with a focus on Lie groups, pseudogroups, and their orbit spaces – and Poisson structures in algebra and geometry and are included here as lecture notes comprising the first two chapters. Following this, chapters combine theoretical and applied perspectives to explore topics at the intersection of differential geometry, differential equations, and category theory. Specific topics covered include:The multisymplectic and variational nature of Monge-Ampère equations in dimension fourIntegrability of fifth-order equations admitting a Lie symmetry algebraApplications of the van Kampen theorem for groupoids to computation of homotopy types of striped surfacesA geometric framework to compare classical systems of PDEs in the category of smooth manifoldsGroups, Invariants, Integrals, and Mathematical Physics is ideal for graduate students and researchers working in these areas. A basic understanding of differential geometry and category theory is assumed.
Groups, Matrices, and Vector Spaces: A Group Theoretic Approach to Linear Algebra
by James B. CarrellTo emphasize the importance of a foundation of knowledge in both geometry and algebra, this text includes an introduction to Euclidean Spaces, and a brief treatment of algebraic topics such as matrix algebra, linear systems, vector spaces, linear coding theory, determinants, eigentheory, group theory, ring theory, and field extensions, even covering an introduction to cryptography.
Groups, Modules, and Model Theory - Surveys and Recent Developments
by László Fuchs Manfred Droste Brendan Goldsmith Lutz StrüngmannThis volume focuses on group theory and model theory with a particular emphasis on the interplay of the two areas. The survey papers provide an overview of the developments across group, module, and model theory while the research papers present the most recent study in those same areas. With introductory sections that make the topics easily accessible to students, the papers in this volume will appeal to beginning graduate students and experienced researchers alike. As a whole, this book offers a cross-section view of the areas in group, module, and model theory, covering topics such as DP-minimal groups, Abelian groups, countable 1-transitive trees, and module approximations. The papers in this book are the proceedings of the conference "New Pathways between Group Theory and Model Theory," which took place February 1-4, 2016, in M#65533;lheim an der Ruhr, Germany, in honor of the editors' colleague R#65533;diger G#65533;bel. This publication is dedicated to Professor G#65533;bel, who passed away in 2014. He was one of the leading experts in Abelian group theory.
Groups, Representations and Physics
by H.F JonesIllustrating the fascinating interplay between physics and mathematics, Groups, Representations and Physics, Second Edition provides a solid foundation in the theory of groups, particularly group representations. For this new, fully revised edition, the author has enhanced the book's usefulness and widened its appeal by adding a chapter on the Cartan-Dynkin treatment of Lie algebras. This treatment, a generalization of the method of raising and lowering operators used for the rotation group, leads to a systematic classification of Lie algebras and enables one to enumerate and construct their irreducible representations. Taking an approach that allows physics students to recognize the power and elegance of the abstract, axiomatic method, the book focuses on chapters that develop the formalism, followed by chapters that deal with the physical applications. It also illustrates formal mathematical definitions and proofs with numerous concrete examples.
Groups, Rings and Group Rings (Lecture Notes in Pure and Applied Mathematics)
by Antonio Giambruno César Polcinn Milies S. K. SehgalThis book is a collection of research papers and surveys on algebra that were presented at the Conference on Groups, Rings, and Group Rings held in Ubatuba, Brazil. This text familiarizes researchers with the latest topics, techniques, and methodologies in several branches of contemporary algebra. With extensive coverage, it examines broad themes f
Groups, Rings, Modules (Dover Books on Mathematics)
by Maurice Auslander David BuchsbaumThis classic monograph is geared toward advanced undergraduates and graduate students. The treatment presupposes some familiarity with sets, groups, rings, and vector spaces. The four-part approach begins with examinations of sets and maps, monoids and groups, categories, and rings. The second part explores unique factorization domains, general module theory, semisimple rings and modules, and Artinian rings. Part three's topics include localization and tensor products, principal ideal domains, and applications of fundamental theorem. The fourth and final part covers algebraic field extensions and Dedekind domains. Exercises are provided at the end of each chapter.
Groups, Rules and Legal Practice
by Rodrigo Eduardo Sánchez BrigidoEver since Hart´s The Concept of Law, legal philosophers agree that the practice of law-applying officials is a fundamental aspect of law. Yet there is a huge disagreement on the nature of this practice. Is it a conventional practice? Is it like the practice that takes place, more generally, when there is a social rule in a group? Does it share the nature of collective intentional action? The book explores the main responses to these questions, and claims that they fail on two main counts: current theories do not explain officials´ beliefs that they are under a duty qua members of an institution, and they do not explain officials´ disagreement about the content of these institutional duties. Based on a particular theory of collective action, the author elaborates then an account of certain institutions, and claims that the practice is an institutional practice of sorts. This would explain officials´ beliefs in institutional duties, and officials´ disagreement about those duties. The book should be of interest to legal philosophers, but also to those concerned with group and social action theories and, more generally, with the nature of institutions.