Defining relations of a group $Gamma= G^{3,4}(2,Z)$ and its action on real quadratic field
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Abstract:
In this paper, we have shown that the coset diagrams for the action of a linear-fractional group $Gamma$ generated by the linear-fractional transformations $r:zrightarrow frac{z-1}{z}$ and $s:zrightarrow frac{-1}{2(z+1)}$ on the rational projective line is connected and transitive. By using coset diagrams, we have shown that $r^{3}=s^{4}=1$ are defining relations for $Gamma$. Furthermore, we have studied some important results for the action of group $Gamma$ on real quadratic field $Q(sqrt{n})$. Also, we have classified all the ambiguous numbers in the orbit.
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Journal title
volume 43 issue 6
pages 1811- 1820
publication date 2017-11-30
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