Abstract
The theory of finite simple groups was for a long time a rather isolated and unusual branch of mathematics. It achieved its goal in 1981 when a proof of the classification theorem was completed. This unique proof, comprising several thousand pages of published articles and preprints, leads to the following list of finite simple groups (see [12] for the details): the groups of Lie type, the alternating groups and the 26 sporadic groups. While each of the first two classes has a uniform description, the groups in the third class still have quite different constructions. The largest sporadic group, called the Monster and denoted F1, was predicted independently by B. Fischer and R. Griess in 1973. It contains 20 or 21 of the sporadic groups and has order >8 – 1053. This group gave rise to many mysteries even before its actual appearance, promising deep connections with different areas of mathematics.
Partially supported by the National Science Foundation through the Mathematical Sciences Research Institute.
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Frenkel, I.B., Lepowsky, J., Meurman, A. (1985). A Moonshine Module for the Monster. In: Lepowsky, J., Mandelstam, S., Singer, I.M. (eds) Vertex Operators in Mathematics and Physics. Mathematical Sciences Research Institute Publications, vol 3. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9550-8_12
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