The Mathieu Groups

The Mathieu Groups are presented in the context of finite geometry and the theory of group amalgams.

A. A. Ivanov (Author)

9781108429788, Cambridge University Press

Hardback, published 21 June 2018

180 pages, 4 b/w illus. 10 tables
23.5 x 15.7 x 1.3 cm, 0.39 kg

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.

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.

Subject Areas: Groups & group theory [PBG], Algebra [PBF], Discrete mathematics [PBD]