The Quotients ofG4,5,120

The groups G4,5, mare significantly useful because they are symmetric groups of the map {4, 5}n, which is constructed from the tessellation {4, 5} of the hyperbolic plane. It is now known (Geom. Ded., 2, 48 (1993), 231–242) that PSL(2, q) is a factor group of the Coxeter groups Gk, l, mif − 1 is a quadratic residue in the Galois field GF(q), where q is a prime power. By using a diagrammatic argument, propounded by Higman, we show that all but finitely many Anand Snare factor groups ofG4,5,120 .