Golden Recursion Inc. logoGolden Recursion Inc. logo
Advanced Search
Monster group

Monster group

A finite simple group that is an algebraic object.

The monster group is an enormous algebraic object used to explain symmetries, such as line and rotation symmetry. It is the largest of the sporadic simple group. The number of elements is 8080, 17424, 79451, 28758, 86459, 90496,17107, 57005, 75436, 80000, 00000 = 246.320.59.76.112.133.17.19.23.29.31.41.47.59.71. The monster group was hypothesized by Bernd Fischer and Robert Greiss. It contains all but six of the other 25 sporadic finite simple groups as subquotients, called the Happy Family.

J-function

The monster group has a connection to the j-function, modular function for SL2(Z) defined on the upper half plane. The Fourier coefficients of j-function turn out to have a decomposition in terms of dimensions of irreducible representations of monster group (196883, 21296876, ...). The monster group's first two dimensions are 1 and 196,883. The j-function's first important coefficient is 196,884, the sum of the monster group's first two dimensions. The connection between the two algebraic objects was discussed in a paper by John Conway and Simon Norton, who termed the connection 'Monstrous Moonshine'. The connection can be made with further dimensions and coefficients from the monster group and j-function.

Timeline

1979
John Conway and Simon Norton write a paper called 'Monstrous Moonshine'.

Further Resources

Title
Author
Link
Type
Date

Group theory and why I love 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000

Web

August 19, 2020

Mathematicians Chase Moonshine, String Theory Connections | Quanta Magazine

Erica Klarreich

Web

March 12, 2015

What is....the Monster?

Richard E. Borcherds

October 2002

References

Golden logo
By using this site, you agree to our Terms & Conditions.