A course in group theory

This book is an excellent and self-contained introduction to the theory of groups, covering all topics likely to be encountered in undergraduate courses. In recent years there has been a great deal of research in group theory and a large number of books have been published. However, most of these are aimed at the postgraduate market and a good introductory text is hard to find. This book aims to fill the gap in the market by providing a comprehensive and clear introduction to the subject. It is written to stimulate and encourage undergraduates (and first year graduates) to further study, and contains numerous worked examples and exercises. This book is intended for first, second and third year undergraduates and first year postgraduates studying group theory.

• Definitions and examples
• Maps and relations on sets
• Elementary consequences of the definitions
• Subgroups
• Cosets and Lagrange's Theorem
• Error-correcting codes
• Normal subgroups and quotient groups
• The Homomorphism Theorem
• Permutations
• The Orbit-Stabilizer Theorem
• The Sylow Theorems
• Applications of Sylow Theorems
• Direct products
• The classification of finite Abelian groups
• The Jordan-Holder Theorem
• Composition factors and chief factors
• Soluble groups
• Examples of soluble groups
• Semi-direct products and wreath products
• Extensions
• Central and cyclic extensions
• Groups with at most 31 elements
• The projective special linear groups
• The Mathieu groups
• The classification of finite simple groups. Appendices: Prerequisites from Number Theory and Linear Algebra
• Groups of order < 32
• Solutions to Exercises.