Editing Modular group (section)

{{Short description|Orientation-preserving mapping class group of the torus}}
{{for|a group whose lattice of subgroups is modular|Iwasawa group}}
{{Group theory sidebar |Discrete}}

In [[mathematics]], the '''modular group'''  is the [[projective linear group|projective special linear group]] <math> \operatorname{PSL}(2,\mathbb Z)</math> of <math>2\times 2</math> [[Matrix (mathematics)|matrices]] with [[integer]] coefficients and [[determinant]] <math>1</math>, such that the matrices <math>A</math> and <math>-A</math> are identified. The modular group acts on the upper-half of the [[complex plane]] by [[linear fractional transformation]]s. The name "modular group" comes from the relation to [[moduli space]]s, and not from [[modular arithmetic]].