The Mathieu Groups

Erscheinungsjahr 2019
ISBN: 978-1-108-42978-8
Verlag: Cambridge University Press

Buch, Englisch, Band 214, 180 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 426 g

Reihe: Cambridge Tracts in Mathematics

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.

Autoren/Hrsg.

Ivanov, A. A.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik

Inhaltsverzeichnis

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.

Über Autor(innen)

Ivanov, A. A.
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.