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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

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