Triangles in the suborbital graphs of the normalizer of $\Gamma_0(N)$

Nazlı Yazıcı Gözütok, Bahadır Özgür Güler

Abstract


In this paper, we investigate a suborbital graph for the normalizer of $\Gamma_0(N) in PSL(2;R)$, where N will be of the form 2^4p^2 such that p > 3 is a prime number. Then we give edge and circuit conditions on graphs arising from the non-transitive action of the normalizer.


Keywords


Congruence subgroups, imprimitive group action, suborbital graphs

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DOI: http://dx.doi.org/10.19184/ijc.2020.4.2.1

References

M. Akbas and D. Singerman, The signature of the normalizer of Γ0(N), Lond. Math. Soc. Lect. Note Ser. 165 (1992), 77–86.

M. Bes ¸enk, B. ¨ O. Güler, and A. Buyukkaya, Suborbital graphs for a non-transitive action of the normalizer, Filomat 33 (2019), 385–392.

N.L. Biggs and A.T. White, Permutation Groups and Combinatorial Structures, Cambridge University Press, Cambridge, 1979.

J.H. Conway and S.P. Norton, Monstrous moonshine, Bull. Lond. Math. Soc. 11 (1977), 308–339.

B. ¨ O. Güler, M. Bes ¸enk and S. Kader, On congruence equations arising from suborbital graphs, Turk. J. Math. 43(5) (2019), 2369–2404.

B. ¨ O. Güler, M. Bes ¸enk, A.H. De˘ ger and S. Kader, Elliptic elements and circuits in suborbital graphs, Hacet. J. Math. Stat. 40(2) (2011), 203–210.

G.A. Jones, D. Singerman and K. Wicks, The modular group and generalized Farey graphs, Lond. Math. Soc. Lect. Note Ser. 160 (1991), 316–338.

S. Kader, Circuits in suborbital graphs for the normalizer, Graphs Combin. 33 (2017), 1531–1542.

R. Keskin, Suborbital graphs for the normalizer Γ0(m), Eur. J. Combin. 27 (2006), 193–206.

R. Keskin and B. Demirtürk, On suborbital graphs for the normalizer of Γ0(m), Electron. J. Combin. 16 (2009), 1–18.

I. Niven, H.S. Zuckerman and H.L. Montgomery, An Introduction to the Theory of Numbers, John Wiley Sons Inc, New York, 1991.

C.C. Sims, Graphs and finite permutation groups, Math. Z. 95 (1967), 76–86.


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