Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3299
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.
Keywords
Modular group, continued fractions, Farey graph
First Page
2751
Last Page
2760
Recommended Citation
DEMİR, BİLAL and KORUOĞLU, ÖZDEN
(2022)
"On parabolic and elliptic elements of the modular group,"
Turkish Journal of Mathematics: Vol. 46:
No.
7, Article 13.
https://doi.org/10.55730/1300-0098.3299
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss7/13
