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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.

First Page

2751

Last Page

2760

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Mathematics Commons

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