The group of Möbius transformations z ↦ (az + b)/(cz + d) under composition, where a,b,c,d are integers and ad − bc = 1. The group is generated by the maps z ↦ z + 1 and z ↦ −1/z and acts on the upper half plane Imz > 0. The modular group can identified with the group SL(2,ℤ) of 2 × 2 matrices with integer entries and determinant 1, provided a matrix is considered equivalent to its negative. See modular form.