Bimonster group

In mathematics, the bimonster is a group that is the wreath product of the monster group M with Z2:

\( Bi = M \wr \mathbb{Z}_2. \, \)

The Bimonster is also a quotient of the Coxeter group corresponding to the Dynkin diagram Y₅₅₅, a Y-shaped graph with 16 nodes:

John H. Conway conjectured that a presentation of the bimonster could be given by adding a certain extra relation to the presentation defined by the Y₅₅₅ diagram; this was proved in 1990 by A. A. Ivanov and Simon P. Norton.

See also

Triality - simple Lie group D4, Y111

References

Basak, Tathagata (2007), "The complex Lorentzian Leech lattice and the Bimonster", Journal of Algebra 309 (1): 32–56, doi:10.1016/j.jalgebra.2006.05.033, MR 2301231.
Conway, John H.; Norton, Simon P.; Soicher, Leonard H. (1988), "The Bimonster, the group Y555, and the projective plane of order 3", Computers in Algebra (Chicago, IL, 1985), Lecture Notes in Pure and Applied Mathematics 111, New York: Dekker, pp. 27–50, MR 1060755.
Conway, J. H.; Pritchard, A. D. (1992), "Hyperbolic reflections for the Bimonster and 3Fi24", Groups, Combinatorics & Geometry (Durham, 1990), London Math. Soc. Lecture Note Ser. 165, Cambridge: Cambridge University Press, pp. 24–45, doi:10.1017/CBO9780511629259.006, MR 1200248.
Conway, John H.; Simons, Christopher S. (2001), "26 implies the Bimonster", Journal of Algebra 235 (2): 805–814, doi:10.1006/jabr.2000.8494, MR 1805481.
Simons, Christopher Smyth (1997), Hyperbolic reflection groups, completely replicable functions, the Monster and the Bimonster, Ph.D. thesis, Princeton University, Department of Mathematics, ISBN 978-0591-50546-7, MR 2696217.
Soicher, Leonard H. (1989), "From the Monster to the Bimonster", Journal of Algebra 121 (2): 275–280, doi:10.1016/0021-8693(89)90064-1, MR 992763.

External links

Weisstein, Eric W., "Bimonster", MathWorld. (Note: incorrectly named here as [36,6,6])

Mathematics Encyclopedia