G-subsets and G-orbits of Q(sqrt n) under action of the modular group

M. Aslam Malik, M. Riaz

It is well known that $G=⟨x,y:x^2=y^3=1⟩$ represents the modular group $PSL(2,Z)$, where $x:z\to \frac{-1}{z},y:z\to \frac{z-1}{z}$ are linear fractiona…