Trees of the Normalizer of Modular Group in the Picard Group

Abstract

In this study, we investigate trees arising from the imprimitive action of the normalizer of Modular

group in the Picard group on extended rational numbers. We determine the farthest vertex from a given vertex

in hyperbolic paths of minimal lengths. We also include some results of the suborbital graph F_{u,N} related to a

continued fraction representation of a rational number.

Keywords

• Normalizer of the modular group,suborbital graphs,continued fraction

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