On suborbital graphs for the normalizer of \(\Gamma _{0}(N)\)
The electronic journal of combinatorics, Tome 16 (2009) no. 1
In this study, we deal with the conjecture given in [R. Keskin, Suborbital graph for the normalizer of $\Gamma _{0}(m)$, European Journal of Combinatorics 27 (2006) 193-206.], that when the normalizer of $\Gamma _{0}(N)$ acts transitively on ${\Bbb Q\cup\{\infty \}}$, any circuit in the suborbital graph $G(\infty,u/n)$ for the normalizer of $\Gamma _{0}(N),$ is of the form $$ v\rightarrow T(v)\rightarrow T^{2}(v)\rightarrow {\ \cdot \cdot \cdot } \rightarrow T^{k-1}(v)\rightarrow v, $$ where $n>1$, $v\in {\Bbb Q\cup \{\infty \}}$ and $T$ is an elliptic mapping of order $k$ in the normalizer of $\Gamma_{0}(N)$.
@article{10_37236_205,
author = {Refik Keskin and Bahar Demirt\"urk},
title = {On suborbital graphs for the normalizer of {\(\Gamma} {_{0}(N)\)}},
journal = {The electronic journal of combinatorics},
year = {2009},
volume = {16},
number = {1},
doi = {10.37236/205},
zbl = {1201.05045},
url = {http://geodesic.mathdoc.fr/articles/10.37236/205/}
}
Refik Keskin; Bahar Demirtürk. On suborbital graphs for the normalizer of \(\Gamma _{0}(N)\). The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/205
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