The Monster Group and Majorana Involutions

A rigorous construction and uniqueness proof for the Monster group, detailing its relation to Majorana involutions.

A. A. Ivanov (Author)

9780521889940, Cambridge University Press

Hardback, published 19 March 2009

266 pages, 15 tables
23.3 x 16 x 2 cm, 0.54 kg

'This book contains the basic knowledge on the Monster group in a very accessible way. some results are published in this book for the first time. Many are not even easily found in literature. Hence the book is a very good source for any group theorist who is interested in sporadic simple groups.' Zentralblatt MATH

This is the first book to contain a rigorous construction and uniqueness proof for the largest and most famous sporadic simple group, the Monster. The author provides a systematic exposition of the theory of the Monster group, which remains largely unpublished despite great interest from both mathematicians and physicists due to its intrinsic connection with various areas in mathematics, including reflection groups, modular forms and conformal field theory. Through construction via the Monster amalgam – one of the most promising in the modern theory of finite groups – the author observes some important properties of the action of the Monster on its minimal module, which are axiomatized under the name of Majorana involutions. Development of the theory of the groups generated by Majorana involutions leads the author to the conjecture that Monster is the largest group generated by the Majorana involutions.

Preface
1. M24 and all that
2. The Monster amalgam M
3. 196 883-representation of M
4. 2-local geometries
5. Griess algebra
6. Automorphisms of Griess algebra
7. Important subgroups
8. Majorana involutions
9. The Monster graph
10. Fischer's story
References
Index.

Subject Areas: Mathematical physics [PHU], Groups & group theory [PBG]