Trees of the normalizer of modular group in Picard group

In this thesis, the suborbital graphs of the normalizer of the Modular group in the Picard group as a result of its group action on the extended set of rational numbers are discussed. Among them, those that do not contain a circuit, i.e. trees, are examined. In the first part, it is emphasized which mathematics sub-disciplines are related to the concepts we use throughout the thesis, and the general elemantary knowledge about this subject is tried to be summarized. Basic information about linear fractional transformations and continuous fractions are given. In the second part, the suborbital graphs of the modular group are detailed since it constitutes a model for our study, then the condition of being a forest means that the suborbital graphs of the normalizer do not contain a circuit has been obtained as a necessary and sufficient condition. Afterwards, the results related to the minimal lengths of trees in these forests, which are an important parameter in terms of graph theory, are obtained.