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

- 2
^{15}· 3^{10}· 5^{3}· 7^{2}· 13 · 19 · 31

- = 90745943887872000

- ≈ 9 · 10
^{16}

The Thomspon group is a subgroup of the Chevalley group E_{8}(F_{3}),
and therefore has a 248 dimensional representation over the field F_{3} 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 F_{3}, giving the embedding of Th into E_{8}(F_{3}).)

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Last updated on Wednesday March 26, 2008 at 21:18:11 PDT (GMT -0700)

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Last updated on Wednesday March 26, 2008 at 21:18:11 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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