A Note on Transitive Action of the Extended Modular Group on Rational Numbers
A Note on Transitive Action of the Extended Modular Group on Rational Numbers
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.
Keywords:
Extended modular group, continued fractions Farey graph.,
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- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2020
- Yayıncı: Mustafa UÇKUN
Sayıdaki Diğer Makaleler
On Bi-f-Harmonic Legendre Curves in Sasakian Space Forms
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Mohammad Irshad KHODABOCUS, Noor-ul-hacq SOOKIA
A Note on Transitive Action of the Extended Modular Group on Rational Numbers