This introductory exposition of group theory by an eminent Russian mathematician is particularly suited to undergraduates, developing material of fundamental importance in a clear and rigorous fashion. The treatment is also useful as a review for more advanced students with some background in group t... read more
Our Editors also recommend:
Group Theory by W. R. Scott Here is a clear, well-organized coverage of the most standard theorems, including isomorphism theorems, transformations and subgroups, direct sums, abelian groups, and more. This undergraduate-level text features more than 500 exercises.
Problems in Group Theory by John D. Dixon Features 431 problems in group theory involving subgroups, permutation groups, automorphisms and finitely generated Abelian groups, normal series, commutators and derived series, solvable and nilpotent groups, and more. Full solutions. 1967 edition.
Elementary Concepts of Topology by Paul Alexandroff Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures.
Linear Algebra and Group Theory by V.I. Smirnov, Richard A. Silverman This accessible text by a Soviet mathematician features material not otherwise available to English-language readers. Its three-part treatment covers determinants and systems of equations, matrix theory, and group theory. 1961 edition.
The Algebraic Structure of Group Rings by Donald S. Passman "Highly recommended" (Bulletin of the London Mathematical Society) and "encyclopedic and lucid" (Bulletin of the American Mathematical Society), this book offers a comprehensive, self-contained treatment of group rings. 1985 edition.
Permutation Groups by Donald S. Passman Lecture notes by a prominent authority provide a self-contained account of classification theorems. Includes work of Zassenhaus on Frobenius elements and sharply transitive groups, Huppert's theorem, more. 1968 edition.
The Theory of Groups by Hans J. Zassenhaus Well-written graduate-level text acquaints reader with group-theoretic methods and demonstrates their usefulness in mathematics. Axioms, the calculus of complexes, homomorphic mapping, p-group theory, more. Many proofs shorter and more transparent than older ones.
Group Theory: The Application to Quantum Mechanics by Paul H. E. Meijer, Edmond Bauer Upper-level undergraduate and graduate students receive an introduction to problem-solving by means of eigenfunction transformation properties with this text, which focuses on eigenvalue problems in which differential equations or boundaries are unaffected by certain rotations or translations. 1965 edition.
Rotations, Quaternions, and Double Groups by Simon L. Altmann This self-contained text presents a consistent description of the geometric and quaternionic treatment of rotation operators, employing methods that lead to a rigorous formulation and offering complete solutions to many illustrative problems.
Character Theory of Finite Groups by I. Martin Isaacs Excellent text approaches characters via rings (or algebras). Focus on properties of characters, role in structure of group. Prerequisite: first-year graduate algebra. 1976 edition.
Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations by Wilhelm Magnus, Abraham Karrass, Donald Solitar A seminal, much-cited account of combinatorial group theory — co-authored by a distinguished teacher of mathematics and a pair of his colleagues — this text for graduate students features numerous helpful exercises. Second, revised 1976 edition.
Group Theory and Chemistry by David M. Bishop Concise, self-contained introduction to group theory and its applications to chemical problems. Symmetry, matrices, molecular vibrations, transition metal chemistry, more. Relevant math included. Advanced-undergraduate/graduate-level. 1973 edition.
Group Theory and Its Application to Physical Problems by Morton Hamermesh 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 physics. With problems.
Lie Groups for Pedestrians by Harry J. Lipkin This book shows how well-known methods of angular momentum algebra can be extended to treat other Lie groups. Chapters cover isospin, the three-dimensional harmonic oscillator, Young diagrams, more. 1966 edition.
Lie Groups, Lie Algebras, and Some of Their Applications by Robert Gilmore This text introduces upper-level undergraduates to Lie group theory and physical applications. It further illustrates Lie group theory's role in several fields of physics. 1974 edition. Includes 75 figures and 17 tables, exercises and problems.
Representation Theory of Finite Groups by Martin Burrow Concise, graduate-level exposition covers representation theory of rings with identity, representation theory of finite groups, more. Exercises. Appendix. 1965 edition.
Theory of Continuous Groups by Charles Loewner These 14 lectures by a renowned educator focus on applications of continuous groups in geometry and analysis. Their unique perspectives are illustrated by numerous inventive geometric examples. 1971 edition.
Product Description:
This introductory exposition of group theory by an eminent Russian mathematician is particularly suited to undergraduates, developing material of fundamental importance in a clear and rigorous fashion. The treatment is also useful as a review for more advanced students with some background in group theory. Beginning with introductory examples of the group concept, the text advances to considerations of groups of permutations, isomorphism, cyclic subgroups, simple groups of movements, invariant subgroups, and partitioning of groups. An appendix provides elementary concepts from set theory. A wealth of simple examples, primarily geometrical, illustrate the primary concepts. Exercises at the end of each chapter provide additional reinforcement.
Reprint of the Hafner Publishing Co., New York, 1959 edition.
This book was printed in the United States of America.
Dover books are made to last a lifetime. Our US book-manufacturing partners produce the highest quality books in the world and they create jobs for our fellow citizens. Manufacturing in the United States also ensures that our books are printed in an environmentally friendly fashion, on paper sourced from responsibly managed forests.
