Turkish Journal of Mathematics
Abstract
The modular group $\Gamma=PSL(2, \mathbf{Z})$ is isomorphic to the free product of two cyclic groups of orders $2$ and $3$. In this paper, we give a necessary and sufficient condition for the existence of elliptic and parabolic elements in $\Gamma$ with a given cusp point. Then we give an algorithm to obtain such elements in words of generators using continued fractions and paths in the Farey graph.
DOI
10.55730/1300-0098.3299
Keywords
Modular group, continued fractions, Farey graph
First Page
2751
Last Page
2760
Recommended Citation
DEMİR, B, & KORUOĞLU, Ö (2022). On parabolic and elliptic elements of the modular group. Turkish Journal of Mathematics 46 (7): 2751-2760. https://doi.org/10.55730/1300-0098.3299
