The theory of groups is simultaneously a branch of abstract algebra and the study of symmetry. Designed to support a reader engaged in a first serious group theory course, or a mathematically mature reader approaching the subject for the first time, this book reviews the essentials. It recaps the basic definitions and results, up to and including Lagrange's Theorem, and then continues to explore topics such as the isomorphism theorems and group actions. Later chapters include material on chain conditions and finiteness conditions, free groups and the theory of presentations. In addition, a novel chapter of "entertainments" takes the basic theory and plays with it to obtain an assortment of results that will show a little of what can be done with the theoretical machinery. Adopting the slightly irreverent tone of Geoff Smith's previous book, Introductory Mathematics: Algebra and Analysis, this book is a key reference that will both stimulate and entertain its readers.
This book reviews the essentials of group theory. It recaps all the basic definitions and results. The author's informal style and irreverent approach has proved popular with students and lecturers alike: his book Introductory Mathematics: Algebra and Analysis is one of SUMS' best-selling titles.
1. The Elements.- 2. Structure.- 3. Action.- 4. Entertainments.- 5. Law.- 6. Presentations.- 7. Appendix A: Fields.- 8. Appendix B: Relations and Orderings.- Further Reading.- Solutions.