The theory of groups / Ian D. Macdonald

This book is intended as a self-contained introduction to group theory for students with no previous knowledge of abstract algebra. Basic properties of groups are developed from a minimal set of axioms. The ideas of homomorphism and isomorphism are introduced early and emphasised throughout.
The structure theorem for finitely generated abelian groups and the Sylow theorems are proved by classical methods, though the modern proofs for the Sylow theorems are given in an appendix. Normal structure, Sylow structure and the interplay between them in finite soluble groups are clearly explained. The approach to free groups is through generators and relations and there is a brief discussion of finitely presented groups. The chapter on nilpotent groups includes some work with commutator identities, a discussion of the Frattini subgroup and theorems characterising groups of exponents 3 and 4. (MathSciNet)

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