The Monster is a Hurwitz group (Q2769821)

A finite group \(G\neq 1\) is called a Hurwitz group if it has generators \(g\), \(h\) satisfying the relations \(g^2=h^3=(gh)^7=1\). In the paper under review the author demonstrates that the Monster sporadic simple group \(M\) is a Hurwitz group. This implies that all sporadic simple groups are Hurwitz groups. In order to prove his result the author uses the 196882-dimensional irreducible representation of \(M\) over \(\mathbb{F}_2\). Rather surprisingly he is able to use this enormous representation effectively in a computer search for the desired generators. The article reports on the algorithmic tools which make it possible to take advantage of the 196882-dimensional representation. Still the search for the generators required the parallel use of processors and a cpu-time of four month.