On Suborbital Graphs for Some Subgroups of the Normalizer of Γ<sub>0</sub>(<i>qp</i><SUP>2</SUP>)

UZUN S., Sanli Z., AKBAŞ M.

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol.47, no.1, pp.157-169, 2021 (SCI-Expanded) identifier identifier


In this paper,we find some certain relationships between the lengths of the circuits in suborbital graphs F-u,F- N for Lambda(N) on (Q) over cap (N) and the periods of the group Lambda(N), generated by Gamma(0)(N) and an Atkin-Lehner involution, which is a subgroup of the normalizer N(Gamma(0)(N)) of Gamma(0)(N) in PSL(2, R) where N will be of the form qp(2), where q = 1 or prime and p is prime > 3 and p not equal q. In this case the action of the nomalizer on the extended rational numbers (Q) over cap is not transitive. And finally, we give some number theoretical results.