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.

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).