M.Sc. Tezi Görüntüleme

Student:	Nazlı YAZICI
Supervisor:	Doç. Dr. Bahadır Özgür GÜLER
Department:	Mathematics
Institution:	Graduate School of Natural and Applied Sciences
University:	Karadeniz Technical University, Turkey

Title of the Thesis:	Suborbital Graphs of The Normalizer of The Modular Group in The Picard Group
Level:	M.Sc.
Acceptance Date:	19/12/2013
Number of Pages:	62
Registration Number:	i2715

Summary:

In this thesis, the suborbital graphs of the normalizer N_P (Γ) of the modular group Γ in the Picard group P acting on extended rational numbers Q ̂ are investigated.

In Chapter 1, we give the general concepts dealing with Topological groups, Hyperbolic geometry, Riemann surfaces, Möbiüs transformations and Graph theory concerning our work. Furthermore, we also give the some definitions and propositions about the ring of Gauss Integers where used in the group action of Picard group.

We obtain the conditions for being an edge and self-paired, then necessary and sufficient conditions for the suborbital graphs to contain a circuit.

Key Words: Modular group, Imprimitive action, Picard group, N_P (Γ), Suborbital graphs.