In mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, the bimonster is a group

Group (mathematics)

In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines any two of its elements to form a third element. To qualify as a group, the set and the operation must satisfy a few conditions called group axioms, namely closure, associativity, identity...

 that is the wreath product

Wreath product

In mathematics, the wreath product of group theory is a specialized product of two groups, based on a semidirect product. Wreath products are an important tool in the classification of permutation groups and also provide a way of constructing interesting examples of groups.Given two groups A and H...

 of the monster group

Monster group

In the mathematical field of group theory, the Monster group M or F1 is a group of finite order:...

 M with Z₂:


The Bimonster is also a quotient of the Coxeter group

Coxeter group

In mathematics, a Coxeter group, named after H.S.M. Coxeter, is an abstract group that admits a formal description in terms of mirror symmetries. Indeed, the finite Coxeter groups are precisely the finite Euclidean reflection groups; the symmetry groups of regular polyhedra are an example...

 corresponding to the Dynkin diagram Y₅₅₅, a Y-shaped graph

Graph theory

In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...

 with 16 nodes:

John H. Conway conjecture

Conjecture

A conjecture is a proposition that is unproven but is thought to be true and has not been disproven. Karl Popper pioneered the use of the term "conjecture" in scientific philosophy. Conjecture is contrasted by hypothesis , which is a testable statement based on accepted grounds...

d that a presentation of the bimonster could be given by adding a certain extra relation; this was proved in 1990 by A. A. Ivanov and Simon P. Norton

Simon P. Norton

Simon Phillips Norton is a mathematician in Cambridge, England, who works on finite simple groups. He constructed the Harada–Norton group, and in 1979 together with John Conway proved there is a connection between the Monster group and the j-function in number theory. They dubbed this monstrous...

.