Problems in Group Theory

This wide-ranging text features 431 problems in group theory, with complete solutions. Topics include subgroups, permutation groups, automorphisms and finitely generated Abelian groups, normal series,

Ma and Gu, both affiliated with the Institute of High Energy Physics in China, explain fundamentals of group theory. A beginning chapter reviews linear algebra, and subsequent chapters cover the conce

This book presents the study of symmetry groups in Physics from a practical perspective, i.e. emphasising the explicit methods and algorithms useful for the practitioner and profusely illustrating by

Essays in Group Theory contains five papers on topics of current interest which were presented in a seminar at MSRI, Berkeley in June, 1985. Special mention should be given to Gromov`s paper, one of t

The theory of groups is simultaneously a branch of abstract algebra and the study of symmetry. Designed for readers approaching the subject for the first time, this book reviews all the essentials. It

Group Theory in Physics - An Introduction is an abridgement and revision of Volumes I and II of the author's previous three volume work Group Theory in Physics. It has been designed to provide a succi

One of the best-written, most skillful expositions of group theory and its physical applications, directed primarily to advanced undergraduate and graduate students in physics, especially quantum phy

An introductory text book for graduates and advanced undergraduates on group representation theory. It emphasizes group theory's role as the mathematical framework for describing symmetry properties o

This volume collects the proceedings of the conference 'Topological methods in group theory', held at Ohio State University in 2014 in honor of Ross Geoghegan's 70th birthday. It consists of eleven peer-reviewed papers on some of the most recent developments at the interface of topology and geometric group theory. The authors have given particular attention to clear exposition, making this volume especially useful for graduate students and for mathematicians in other areas interested in gaining a taste of this rich and active field. A wide cross-section of topics in geometric group theory and topology are represented, including left-orderable groups, groups defined by automata, connectivity properties and Σ-invariants of groups, amenability and non-amenability problems, and boundaries of certain groups. Also included are topics that are more geometric or topological in nature, such as the geometry of simplices, decomposition complexity of certain groups, and problems in shape theory.

Reversibility is a thread woven through many branches of mathematics. It arises in dynamics, in systems that admit a time-reversal symmetry, and in group theory where the reversible group elements are those that are conjugate to their inverses. However, the lack of a lingua franca for discussing reversibility means that researchers who encounter the concept may be unaware of related work in other fields. This text is the first to make reversibility the focus of attention. The authors fix standard notation and terminology, establish the basic common principles, and illustrate the impact of reversibility in such diverse areas as group theory, differential and analytic geometry, number theory, complex analysis and approximation theory. As well as showing connections between different fields, the authors' viewpoint reveals many open questions, making this book ideal for graduate students and researchers. The exposition is accessible to readers at the advanced undergraduate level and above.

Geometric group theory is a vibrant subject at the heart of modern mathematics. It is currently enjoying a period of rapid growth and great influence marked by a deepening of its fertile interactions with logic, analysis and large-scale geometry, and striking progress has been made on classical problems at the heart of cohomological group theory. This volume provides the reader with a tour through a selection of the most important trends in the field, including limit groups, quasi-isometric rigidity, non-positive curvature in group theory, and L2-methods in geometry, topology and group theory. Major survey articles exploring recent developments in the field are supported by shorter research papers, which are written in a style that readers approaching the field for the first time will find inviting.

This book, first published in 1990, gives a general account of diagram manipulation techniques, as alternatives to algebraic methods of proof, in theoretical physics. Methods reviewed by the author include the popular techniques pioneered by Jucys and collaborators in the quantum theory of angular momentum and by Feynman in quantum field theory. The reader is encouraged to become bilingual in that many steps in the argument are presented as Problems, and are immediately followed by solutions and by comments on the method or proof and the significance of the results. This book will be of value to graduate students and research workers in theoretical solid state physics, atomic, molecular, nuclear and particle physics and theoretical chemistry.

This text introduces readers to the theory and research findings needed to understand how to make groups effective, and it helps build the skills required to apply that knowledge in practical situati

This informative and exhaustive study gives a problem-solving approach to the difficult subject of analytic number theory. It is primarily aimed at graduate students and senior undergraduates. The goa

This informative and exhaustive study gives a problem-solving approach to the difficult subject of analytic number theory. It is primarily aimed at graduate students and senior undergraduates. The goa

After the pioneering work of Brauer in the middle of the 20th century in the area of the representation theory of groups, many entirely new developments have taken place and the field has grown into a

This book presents an up-to-date account of research in important topics of fuzzy group theory. It concentrates on the theoretical aspects of fuzzy subgroups of a group. It includes applications to ab

While it is nearly impossible to answer how exactly one does mathematical research, it is no exaggeration to say that the ability to do it effectively lies in asking "well-posed" questions. This book

Mathematics is kept alive by the appearance of new, unsolved problems. This book provides a steady supply of easily understood, if not easily solved, problems that can be considered in varying depths

Developed at Babes Bolyai University in Romania, this graduate text consists of ten chapters that review the basic notions and terminology of Abelian group theory, then list 20-80 exercises for practi

In this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major

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.

In this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major

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.

This volume reflects the fruitful connections between group theory and topology. It contains articles on cohomology, representation theory, geometric and combinatorial group theory. Some of the world's best known figures in this very active area of mathematics have made contributions, including substantial articles from Ol'shanskii, Mikhajlovskii, Carlson, Benson, Linnell, Wilson and Grigorchuk, which will be valuable reference works for some years to come. Pure mathematicians working in the fields of algebra, topology, and their interactions, will find this book of great interest.

The classification of the finite simple groups is one of the major intellectual achievements of this century, but it remains almost completely unknown outside of the mathematics community. This introd

Concise, self-contained introduction to group theory and its applications to chemical problems. Symmetry, symmetry operations, point groups, matrices, matrix representations, equivalent and reducible

The isomorphism problem of ergodic theory has been extensively studied since Kolmogorov's introduction of entropy into the subject and especially since Ornstein's solution for Bernoulli processes. Much of this research has been in the abstract measure-theoretic setting of pure ergodic theory. However, there has been growing interest in isomorphisms of a more restrictive and perhaps more realistic nature which recognize and respect the state structure of processes in various ways. These notes give an account of some recent developments in this direction. A special feature is the frequent use of the information function as an invariant in a variety of special isomorphism problems. Lecturers and postgraduates in mathematics and research workers in communication engineering will find this book of use and interest.

In 1977 several eminent mathematicians were invited to Durham to present papers at a short conference on homological and combinatorial techniques in group theory. The lectures, published here, aimed at presenting in a unified way new developments in the area. Group theory is approached from a geometrical viewpoint and much of the material has not previously been published. The various ways in which topological ideas can be used in group theory are also brought together. The volume concludes with an extensive set of problems, ranging from explicit questions demanding detailed calculation to fundamental questions motivating research in the area. These lectures will be of interest mainly to researchers in pure mathematics but will also prove useful in connection with relevant postgraduate courses.

The theory of abstract groups comes into play in an astounding number of seemingly unconnected areas like crystallography and quantum mechanics, geometry and topology, analysis and algebra, physics,