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Finite

Thompson group (finite)

In the mathematical field of group theory, the Thompson group Th (found by John G. Thompson) is a sporadic simple group of order

   215 · 310 · 53 · 72 · 13 · 19 · 31
= 90745943887872000
≈ 9 · 1016

The Thomspon group is a subgroup of the Chevalley group E8(F3), and therefore has a 248 dimensional representation over the field F3 with 3 elements, which was used to construct it. The centralizer of an element of order 3 of type 3C in the Monster group is a product of the Thompson group and a group of order 3, as a result of which the Thompson group acts on a vertex operator algebra over the field with 3 elements. (This vertex operator algebra contains the E8 Lie algebra over F3, giving the embedding of Th into E8(F3).)

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