Monster group

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Monster group

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Monster group

1. (algebra) The largest sporadic group, of order 2⁴⁶ · 3²⁰ · 5⁹ · 7⁶ · 11² · 13³ · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71 (approximately 8 · 10⁵³), denoted M or F₁.
   • 1996, Michael P. Tuite, “Monstrous Moonshine and orbifolds”, in K.T. Arasu, J.F. Dillon, K. Harada, S. Sehgal, R. Solomon, editors, Groups, Difference Sets, and the Monster: Proceedings of a Special Research Quarter, Walter de Gruyter, page 443:

     We next consider the possible ${\displaystyle \mathbb {Z} _{n}}$ orbifoldings of ${\displaystyle {\mathcal {V}}^{2}}$ with respect to elements of the Monster group M [Tul].

   • 2008, L. J. P. Kilford, Modular Forms: A Classical and Computational Introduction, Imperial College Press, page 106:

     We note that ${\displaystyle c(1)=196883}$; this is not just a numerological coincidence, but follows from a branch of mathematics called moonshine theory which arises from string theory and relates the Monster group and modular functions.

   • 2014, Martin Schlichenmaier, Krichever-Novikov Type Algebras: Theory and Applications, Walter de Gruyter, page 340:

     They were also crucial in understanding the Monster and Moonshine phenomena, which refers to the fact that the dimensions of the irreducible representations of the largest sporadic finite group, the monster group, show up in the q-expansion coefficients of the elliptic modular function j.

• (the largest sporadic group): Fischer–Griess Monster, friendly giant

• baby monster group

• monstrous moonshine
• supersingular prime

• Baby monster group on Wikipedia.Wikipedia
• Monstrous moonshine on Wikipedia.Wikipedia
• Supersingular prime on Wikipedia.Wikipedia
• Monster Group on Wolfram MathWorld