Topics in Group Theory

1. Front Matter

   Pages i-xvi

   PDF

2. The Elements

   • Geoff C. Smith, Olga M. Tabachnikova

   Pages 1-41

3. Structure

   • Geoff C. Smith, Olga M. Tabachnikova

   Pages 43-87

4. Action

   • Geoff C. Smith, Olga M. Tabachnikova

   Pages 89-124

5. Entertainments

   • Geoff C. Smith, Olga M. Tabachnikova

   Pages 125-158

6. Law

   • Geoff C. Smith, Olga M. Tabachnikova

   Pages 159-188

7. Presentations

   • Geoff C. Smith, Olga M. Tabachnikova

   Pages 189-217

8. Appendix A: Fields

   • Geoff C. Smith, Olga M. Tabachnikova

   Pages 219-228

9. Appendix B: Relations and Orderings

   • Geoff C. Smith, Olga M. Tabachnikova

   Pages 229-238

10. Back Matter

    Pages 239-255

    PDF

We very much hope that this book will be read by the interested student (and not just be parked on a shelf for occasional consultation). If you want a comprehensive reference book on Group Theory, do not buy this text. There are much better books available, some of which are mentioned below. We have a tale to tell; the absolute essentials of the theory of groups, followed by some entertainments and some more advanced material. The theory of groups is an enormous body of material which interacts with other branches of mathematics at countless frontiers. Some parts of the theory are essentially complete, but in other areas all we see are questions. People happily read novels, so why not mathematics books? When math­ ematics was studied by only a few people, there was less need to try to write attractively or encouragingly since the likely readership consisted of a small group of highly motivated individuals who needed little encouragement. Even so, many talented academic writers managedto write brilliantly because they knew no other way. As higher education has opened up in economically devel­ oped countries, a much more diverse collection of people is exploring advanced mathematics and science. The challenge for authors is to produce books which engage this wider community without compromising the content.

• Abstract algebra
• Symmetry
• algebra
• group action
• group theory

“The authors succeed to simplify a number of standard proofs through fresh elementary arguments. Very lucid writing provides the reader with reasons for performing every step in the proofs. … reading the book was a delight … To summarize: this is one of the best texts in mathematics I got my hands on.” (M.Deaconescu, zbMATH 0953.20001, 2021)

• School of Mathematical Sciences, University of Bath, Bath, UK

  Geoff C. Smith, Olga M. Tabachnikova

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