An Introduction to the Theory of Groups

Book Details:

• Publisher: Dover

• Author: G. M. Petersen, Paul S. Alexandroff, Hazel Perfect, Paul Alexandroff

• Language: English

• ISBN: 9780486488134

• Pages: 112

• Cover: Paperback

• Dimensions: 8.5 x 5.5 x 0.4 inches

About The Book:

This accessible and introductory exposition of group theory, written by eminent Russian mathematicians G. M. Petersen, Paul S. Alexandroff, Hazel Perfect, and Paul Alexandroff, is perfectly suited for undergraduates and those looking for a clear and rigorous treatment of the subject. With a focus on fundamental concepts, the book is also valuable as a review for more advanced students who have some background in group theory.

The text begins with introductory examples of the group concept and gradually advances to more complex topics, such as groups of permutations, isomorphism, cyclic subgroups, and simple groups of movements. It further explores invariant subgroups and the partitioning of groups, providing a thorough understanding of the building blocks of group theory.

A wealth of simple examples, primarily drawn from geometry, helps to illustrate key concepts, making them easier to understand and apply. The book also includes exercises at the end of each chapter, providing further reinforcement and an opportunity for practice. An appendix offers elementary concepts from set theory, ensuring readers have the foundational knowledge required for group theory.

This text is an excellent resource for students new to group theory, as well as those seeking a rigorous, yet accessible, introduction to the subject. Whether used as a textbook for a course or as a supplementary reference, it serves as an invaluable guide for understanding the core principles of group theory.