Fundamentals of Group Theory: An Advanced Approach

Chapter headings: • 1 Preliminaries • 2 Groups and Subgroups • 3 Cosets, Index and Normal Subgroups • 4 Homomorphisms, Chain Conditions and Subnormality • 5 Direct and Semidirect Products • 6 Permutation Groups • 7 Group Actions; The Structures of p-Groups • 8 Sylow Theory • 9 The Classification Problem for Groups • 10 Finiteness Conditions • 11 Solvable and Nilpotent Groups • 12 Free Groups and Presentations • 13 Abelian Groups • References • List of Symbols • Index

Fundamentals of Group Theory provides a comprehensive account of the basic theory of groups. Both classic and unique topics in the field are covered, such as an historical look at how Galois viewed groups, a discussion of commutator and Sylow subgroups, and a presentation of Birkhoff’s theorem. Written in a clear and accessible style, the work presents a solid introduction for students wishing to learn more about this widely applicable subject area. This book will be suitable for graduate courses in group theory and abstract algebra and will also have appeal to advanced undergraduates. In addition, it will serve as a valuable resource for those pursuing independent study. Group Theory is a timely and fundamental addition to literature in the study of groups.