The Mathieu Groups
Seiten
2018
Cambridge University Press (Verlag)
978-1-108-42978-8 (ISBN)
Cambridge University Press (Verlag)
978-1-108-42978-8 (ISBN)
This book provides a wealth of insight into the fascinating theory surrounding the Mathieu groups. In particular, the author introduces the theory of group amalgams and gives a systematic account of 'small groups'. Postgraduate students and researchers will enjoy this unique geometric treatment of these well-known finite simple groups.
The Mathieu groups have many fascinating and unusual characteristics and have been studied at length since their discovery. This book provides a unique, geometric perspective on these groups. The amalgam method is explained and used to construct M24, enabling readers to learn the method through its application to a familiar example. The same method is then used to construct, among others, the octad graph, the Witt design and the Golay code. This book also provides a systematic account of 'small groups', and serves as a useful reference for the Mathieu groups. The material is presented in such a way that it guides the reader smoothly and intuitively through the process, leading to a deeper understanding of the topic.
The Mathieu groups have many fascinating and unusual characteristics and have been studied at length since their discovery. This book provides a unique, geometric perspective on these groups. The amalgam method is explained and used to construct M24, enabling readers to learn the method through its application to a familiar example. The same method is then used to construct, among others, the octad graph, the Witt design and the Golay code. This book also provides a systematic account of 'small groups', and serves as a useful reference for the Mathieu groups. The material is presented in such a way that it guides the reader smoothly and intuitively through the process, leading to a deeper understanding of the topic.
A. A. Ivanov is Professor of Pure Mathematics in the Department of Mathematics at Imperial College London. His main research interest is the sporadic simple groups, and he has published four books on the subject.
1. The Mathieu group M24 as we knew it; 2. Amalgam method; 3. L4(2) in two incarnations and L3(4); 4. From L5(2) to the Mathieu amalgam; 5. M24 as universal completion; 6. Maximal subgroups; 7. 45-representation of M24; 8. The Held group; 9. Inevitability of Mathieu groups; 10. Locally projective graphs and amalgams; Index.
| Erscheinungsdatum | 18.08.2018 |
|---|---|
| Reihe/Serie | Cambridge Tracts in Mathematics |
| Zusatzinfo | Worked examples or Exercises; 10 Tables, black and white; 4 Line drawings, black and white |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 157 x 235 mm |
| Gewicht | 390 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| ISBN-10 | 1-108-42978-5 / 1108429785 |
| ISBN-13 | 978-1-108-42978-8 / 9781108429788 |
| Zustand | Neuware |
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