A Course in the Theory of Groups

Graduate Texts in Mathematics #80

by Derek J.S. Robinson

A Course in the Theory of Groups is a comprehensive introduction to the theory of groups - finite and infinite, commutative and non-commutative. Presupposing only a basic knowledge of modern algebra, it introduces the reader to the different branches of group theory and to its principal accomplishments. While stressing the unity of group theory, the book also draws attention to connections with other areas of algebra such as ring theory and homological algebra.
This new edition has been updated at various points, some proofs have been improved, and lastly about thirty additional exercises are included. There are three main additions to the book. In the chapter on group extensions an exposition of Schreier's concrete approach via factor sets is given before the introduction of covering groups. This seems to be desirable on pedagogical grounds. Then S. Thomas's elegant proof of the automorphism tower theorem is included in the section on complete groups. Finally an elementary counterexample to the Burnside problem due to N.D. Gupta has been added in the chapter on finiteness properties.

Genres: Mathematics, Theory

519 pages, Paperback

First published August 1, 1993

Reviews

[Jerzy · Rating 1 out of 5]

Together with an incomprehensible instructor who covered the material way too fast, this unreadable book killed my dreams of becoming a mathematician. Temporarily, anyway. And I'm sure if I'd gone slower, and had a little stronger background, and actually had time to try my hand at solving all of the problems, the course would have been okay... but even if it's a good reference book, I would definitely be wary of any course that uses this unless you're very well prepared. I do not recommend this as a good introductory or self-study textbook.