An Introduction to the Theory of Groups
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.
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An Introduction to the Theory of Groups
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.
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An Introduction to the Theory of Groups

An Introduction to the Theory of Groups

An Introduction to the Theory of Groups

An Introduction to the Theory of Groups

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Overview

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.

Product Details

ISBN-13: 9780486488134
Publisher: Dover Publications
Publication date: 04/19/2012
Series: Dover Books on Mathematics
Pages: 128
Product dimensions: 5.20(w) x 8.30(h) x 0.30(d)

About the Author

The prominent Russian mathematician Paul S. Alexandroff (1896–1982) was primarily associated with the University of Moscow. He contributed to the areas of topology and homology theory and was the author of Dover's Elementary Concepts in Topology (60747-X). 

Table of Contents

1. The Group Concept
2. Groups of Permutations
3. Some General Remarks about Groups. The Concept of Isomorphism
4.Cyclic Subgroups of a Given Group
5. Simple Groups of Moments
6. Invariant Subgroups
7.Homomorphic Mappings
8. Partioningof a Group Relative to a Given Subgroup. Difference Modules
Appendix
Books to Cosult
Index
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