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Groupes finis, séries formelles et fonctions modulaires. (French) Zbl 0554.20001

Sémin. sur les groupes finis, Tome I, Publ. Math. Univ. Paris VII 14, 105-127 (1983).
[For the entire collection see Zbl 0549.00007.]
In 1978/79 Conway and Thompson, following interesting remarks of McKay and Ogg, discovered a remarkable relationship between the theory of finite simple groups, and in particular of the Fischer-Griess ”Monster group” on the one hand, and the theory of modular functions on the other. This has led to a great deal of work by many people through which the majority of the facts observed have been proved, although not by any means ’explained’. The paper under review gives a very clear, careful (except for some misprints) and detailed survey of the present state of knowledge and in particular of the relationship of the modular functions involved with theta-functions.
Reviewer: S.J.Patterson

MSC:

20D08 Simple groups: sporadic groups
11F03 Modular and automorphic functions

Citations:

Zbl 0549.00007