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 The author provides a systematic exposition of the theory of the Monster group, which remains largely unpublished despite great interest from both mathematicians and physicists due to its intrinsic connection with various areas in mathematics, including reflection groups,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.
A. A. Ivanov is a Professor in the Mathematical Department at Imperial College, London and the Institute of System Analysis at the Russian Academy of Sciences, Moscow.
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.