Circuits in Suborbital Graphs for The Normalizer

Kader, Serkan

doi:10.1007/s00373-017-1852-x

Cited by 9 publications

(5 citation statements)

References 8 publications

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“…The subgroup Γ 0 (N ) = {g ∈ Γ : c ≡ 0 (mod N )} is a well-known congruence subgroup of the classical modular group Γ. The normalizer of Γ 0 (N ) in P SL(2, R) turns to be a very important group in the study of moonshine and for this reason has been studied by many authors (see, for example, [4,5,8,13,14]). It consists exactly of the matrices…”

Section: Preliminariesmentioning

confidence: 99%

Hexagonal cell graphs of the normalizer with signature $(2, 6, \infty)$

Gözütok

Jeribi

2022

Hacettepe Journal of Mathematics and Statistics

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In this paper, we investigate suborbital graphs G u,n of the normalizer Γ B (N ) of Γ 0 (N ) in P SL(2, R) for N = 2 α 3 β , where α = 0, 2, 4, 6 and β = 1, 3. In each of these cases, the normalizer becomes a triangle group and the graph arising from the action of the normalizer contains hexagonal circuits. In order to obtain graphs, we first define an imprimitive action of Γ B (N ) on Q using the group H B (N ) and then we obtain some properties of the graphs arising from this action.

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Section: Preliminariesmentioning

confidence: 99%

Hexagonal cell graphs of the normalizer with signature $(2, 6, \infty)$

Gözütok

Jeribi

2022

Hacettepe Journal of Mathematics and Statistics

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“…In a series of papers, suborbital graphs of the normalizer were also studied under various restrictions by the same idea [3,12,13]. Then, nontransitive cases have been examined to reach the general statement [7,10,11]. An interesting contribution of these studies was that the action of normalizer offers solutions for some congruence equations dealing with the sizes of circuits in the suborbital graph [8].…”

Section: Motivationmentioning

confidence: 99%

On congruence equations arising from suborbital graphs

Güler¹,

Beşenk²,

Kader³

2019

Turk J Math

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In this paper we deal with congruence equations arising from suborbital graphs of the normalizer of Γ0(m) in P SL(2, R) . We also propose a conjecture concerning the suborbital graphs of the normalizer and the related congruence equations. In order to prove the existence of solution of an equation over prime finite field, this paper utilizes the Fuchsian group action on the upper half plane and Farey graphs properties.

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“…Many researchers have conducted studies [2][3][4][5][6][7] that reveal the relationship of many groups of graphswith the methods and results presented in this study. In particular, because of the interesting nature of the normalizer Γ B (N) of Γ 0 (N) in PSL(2, R) [8][9][10] and its complexity relative to the modular group, researchers have studied normalizer-related graphs under various conditions [2,[11][12][13].…”

Section: Introductionmentioning

confidence: 99%