On Suborbital Graphs for Some Subgroups of the Normalizer of Γ₀(<i>qp</i><SUP>2</SUP>)

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UZUN S., Sanli Z., AKBAŞ M.

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

• Publication Type: Article / Article
• Volume: 47 Issue: 1
• Publication Date: 2021
• Doi Number: 10.1007/s41980-020-00373-x
• Journal Name: BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
• Page Numbers: pp.157-169
• Karadeniz Technical University Affiliated: Yes

Abstract

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.