Group Theory Finite Discrete Groups And Applications
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Group Theory Finite Discrete Groups And Applications
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Author : Ioannis John Demetrius Vergados
language : en
Publisher: World Scientific
Release Date : 2023-06-28
Group Theory Finite Discrete Groups And Applications written by Ioannis John Demetrius Vergados and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-28 with Science categories.
This book deals with the role played by symmetry in the understanding of the physical world, beginning with the notion of geometric symmetries of the ancient Greek philosophers and mathematicians. The recognition of the existence of symmetries led to the notion of transformations, which led from one state of the system to another. It was then realized that such transformations, under the operation of multiplication, constitute an interesting set, whose study led to the branch of mathematics known as Group Theory. With the emergence of quantum mechanics, this theory became much more interesting and led to some additional applications. The theory got another boost with the need for of the internal degrees of freedom in describing physical systems. This way the notion of symmetry is no longer purely geometric and evolved into a useful tool in the study of all physical sciences.For practical reasons as well as pedagogical reasons, group theory is usually split into two parts. The first deals with discrete groups, with the group elements being countable, usually finite in number, while the second deals with continuous groups, whose elements depend on continuous parameters. This volumefocuses the discussion on discrete groups. Given that group theory should be presented from a unified perspective, involving not only the mathematical rigor and beauty of symmetries, but also the ability to use it as a tool for applications, either currently popular or expected to become so in the future, this approach will surely be more beneficial to the dedicated reader. It is not intended for those who would like to just look up a formula or use the results of a table, without understanding their derivation.
Theory Of Finite Groups
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Author : Laurens Jansen
language : en
Publisher:
Release Date : 1967
Theory Of Finite Groups written by Laurens Jansen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Finite groups categories.
Finite Group Theory
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Author : M. Aschbacher
language : en
Publisher: Cambridge University Press
Release Date : 2000-06-26
Finite Group Theory written by M. 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 2000-06-26 with Mathematics categories.
The book provides the basic foundations for the local theory of finite groups, the theory of classical linear groups, and the theory of buildings and BN-pairs.
Handbook Of Computational Group Theory
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Author : Derek F. Holt
language : en
Publisher: CRC Press
Release Date : 2005-01-13
Handbook Of Computational Group Theory written by Derek F. Holt and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-13 with Mathematics categories.
The origins of computation group theory (CGT) date back to the late 19th and early 20th centuries. Since then, the field has flourished, particularly during the past 30 to 40 years, and today it remains a lively and active branch of mathematics. The Handbook of Computational Group Theory offers the first complete treatment of all the fundame
The Atlas Of Finite Groups Ten Years On
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Author : Robert Curtis
language : en
Publisher: Cambridge University Press
Release Date : 1998-06-11
The Atlas Of Finite Groups Ten Years On written by Robert Curtis 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 1998-06-11 with Mathematics categories.
Proceedings containing twenty articles by leading experts in group theory and its applications.
Representation Theory Of Finite Groups
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Author : Benjamin Steinberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-23
Representation Theory Of Finite Groups written by Benjamin Steinberg 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 2011-10-23 with Mathematics categories.
This book is intended to present group representation theory at a level accessible to mature undergraduate students and beginning graduate students. This is achieved by mainly keeping the required background to the level of undergraduate linear algebra, group theory and very basic ring theory. Module theory and Wedderburn theory, as well as tensor products, are deliberately avoided. Instead, we take an approach based on discrete Fourier Analysis. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject. A number of exercises are included. This book is intended for a 3rd/4th undergraduate course or an introductory graduate course on group representation theory. However, it can also be used as a reference for workers in all areas of mathematics and statistics.
Introduction To Group Theory
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Author : Oleg Vladimirovič Bogopolʹskij
language : en
Publisher: European Mathematical Society
Release Date : 2008
Introduction To Group Theory written by Oleg Vladimirovič Bogopolʹskij and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This book quickly introduces beginners to general group theory and then focuses on three main themes : finite group theory, including sporadic groups combinatorial and geometric group theory, including the Bass-Serre theory of groups acting on trees the theory of train tracks by Bestvina and Handel for automorphisms of free groups With its many examples, exercises, and full solutions to selected exercises, this text provides a gentle introduction that is ideal for self-study and an excellent preparation for applications. A distinguished feature of the presentation is that algebraic and geometric techniques are balanced. The beautiful theory of train tracks is illustrated by two nontrivial examples. Presupposing only a basic knowledge of algebra, the book is addressed to anyone interested in group theory: from advanced undergraduate and graduate students to specialists.
Discrete Groups And Geometry
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Author : William J. Harvey
language : en
Publisher: Cambridge University Press
Release Date : 1992-07-30
Discrete Groups And Geometry written by William J. Harvey 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 1992-07-30 with Mathematics categories.
This book constitutes the proceedings of a conference held at the University of Birmingham to mark the retirement of Professor A. M. Macbeath. The papers represent up-to-date work on a broad spectrum of topics in the theory of discrete group actions, ranging from presentations of finite groups through the detailed study of Fuchsian and crystallographic groups, to applications of group actions in low dimensional topology, complex analysis, algebraic geometry and number theory. For those wishing to pursue research in these areas, this volume offers a valuable summary of contemporary thought and a source of fresh geometric insights.
Discrete Subgroups Of Semisimple Lie Groups
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Author : Gregori A. Margulis
language : en
Publisher: Springer Science & Business Media
Release Date : 1991-02-15
Discrete Subgroups Of Semisimple Lie Groups written by Gregori A. Margulis 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 1991-02-15 with Mathematics categories.
Discrete subgroups have played a central role throughout the development of numerous mathematical disciplines. Discontinuous group actions and the study of fundamental regions are of utmost importance to modern geometry. Flows and dynamical systems on homogeneous spaces have found a wide range of applications, and of course number theory without discrete groups is unthinkable. This book, written by a master of the subject, is primarily devoted to discrete subgroups of finite covolume in semi-simple Lie groups. Since the notion of "Lie group" is sufficiently general, the author not only proves results in the classical geometry setting, but also obtains theorems of an algebraic nature, e.g. classification results on abstract homomorphisms of semi-simple algebraic groups over global fields. The treatise of course contains a presentation of the author's fundamental rigidity and arithmeticity theorems. The work in this monograph requires the language and basic results from fields such as algebraic groups, ergodic theory, the theory of unitary representatons, and the theory of amenable groups. The author develops the necessary material from these subjects; so that, while the book is of obvious importance for researchers working in related areas, it is essentially self-contained and therefore is also of great interest for advanced students.
Theory And Applications Of Finite Groups
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Author : George Abram Miller
language : en
Publisher:
Release Date : 1919
Theory And Applications Of Finite Groups written by George Abram Miller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1919 with Group theory categories.