Topics in Group Theory / Edition 1by Geoff Smith, Olga Tabachnikova, G. C. Smith
Pub. Date: 05/15/2000
Publisher: Springer London
The theory of groups is simultaneously a branch of abstract algebra and the study of symmetry. Designed for readers approaching the subject for the first time, this book reviews all the essentials. It recaps the basic definitions and results, including Lagranges Theorem, 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" demonstrates an assortment of results that can be achieved with the theoretical machinery.
Table of Contents1. 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.
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Excellent textbook to complement any formal text for use in class with an introductory course on Group Theory...a great supplement to any engineering student of information and coding theory that desires to explore the further backgrounds of the development of codes and ciphers from the abstract algebraic subjects of Galois Fields, Rings, Topology, and Group Theory...gives a good overview of elements, groups, sets, rings, fields, as applied to much deeper subjects like symmetry, isomorphisms, topology, knot theory, etc...good problem sets at the conclusion of each chapter with worked solutions at the end of the book...another good textbok in the SUMS (Springer Undergraduate Matematics Series)...