Modular group
![](/Images/godic/202501/27/Cyclic_group.svg0305.png")
![The braid group B3 is the universal central extension of the modular group.](/Images/godic/202501/27/Braid-modular-group-cover.svg0305.png")
![A typical fundamental domain for the action of Γ on the upper half-plane.](/Images/godic/202501/27/ModularGroup-FundamentalDomain-010305.png")
![Visualization of the map (2,3,∞) → (2,3,7) by morphing the associated tilings.[5]](/Images/godic/202501/27/Morphing_of_modular_tiling_to_2_3_7_triangle_tiling0305.gif")
In mathematics, the modular group is the projective special linear group PSL(2,Z) of 2 x 2 matrices with integer coefficients and unit determinant. The matrices A and -A are identified. The modular group acts on the upper-half of the complex plane by fractional linear transformations, and the name "modular group" comes from the relation to moduli spaces and not from modular arithmetic.