Resource:Books in elementary group theory

This page lists books that cover a first-course or equivalent in group theory. Some of these courses cover a lot more than the material usually done in a first course.

The book Algebra by Michael Artin is one of the stnadard references for elementary algebra, including linear algebra, group theory, and ring theory. It was the top reference in the United States till a few years ago.

Artin's group theory-related chapters are:


 * The second chapter covers the basic definitions of group, homomorphism etc.
 * The third chapter goes a little further into group theory
 * The fifth chapter goes into group actions
 * The sixth chapter covers Sylow theorems

The main features of Artin's style of presentation are:


 * The focus is a lot on examples and recovering the definition from the examples
 * The style of writing is more like an informal classroom exposition than like a formal textbook. Textbook-style clarity may thus be sacrificed somewhat
 * There are lots of exercises, many of them harder than they first appear
 * A lot of emphasis is placed on group actions, possibly leading to a corresponding de-emphasis on the abstract structure of the group

Dummit and Foote's text has the first six chapters directly devoted to group theory. These include a bit about almost all aspects of the theory of finite groups, with an extensive discussion of Sylow theory, as well as things like nilpotent groups and solvable groups.

The main feature of their style of presentation is:


 * There is a lot of focus on the abstract existence of a group, as well as focus on the theory of groups and subgroups. In fact, the approach taken by Dummit and Foote is very close to that taken by Herstein, but with a lot more elaboration and elucidation
 * There are many unsolved problems, but most of them are not as hard as those in the books by Artin and Herstein. Usually most of them do not require great ingenuity to solve and can be done by applying ideas already discussed in the main text

This is one of the classical books in group theory, and was used as a college text in American universities a generation ago. It is famous for its hard problems.