The extended modular group $\overline{\Gamma}$ is isomorphic to the amalgamated free product of two dihedral groups $D_2$ and $D_3$ with amalgamation $\mathbb{Z}_2$. This group acts on rational numbers transitively. In this study, we obtain elements in the extended modular group that are mappings between given two rationals. Also, we express these elements as a word in generators. We use interesting relations between continued fractions and the Farey graph.
Birincil Dil | İngilizce |
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Konular | Matematik |
Bölüm | Research Articles |
Yazarlar | |
Yayımlanma Tarihi | 28 Temmuz 2022 |
Yayımlandığı Sayı | Yıl 2022 Cilt: 3 Sayı: 2 |
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