Ph.D. Tezi Görüntüleme

Student:	Serkan KADER
Supervisor:	Prof. Dr. Mehmet AKBAŞ
Department:	Matematik
Institution:	Graduate School of Natural and Applied Sciences
University:	Karadeniz Technical University, Turkey

Title of the Thesis:	Signatures of the NEC Groups and Graphs
Level:	Ph.D.
Acceptance Date:	28/3/2008
Number of Pages:	83
Registration Number:	Di631

Summary:

In this thesis, our main purpose is to find signatures of some Fuchsian groups of the group PSL(2,IR) by considering suborbital graphs.

In Chapter 1, the structure of Non-Euclidean Crystalllographic Groups is discussed and some properties of PSL(2,IR),Gamma-Modular group, congruence subgroups, normalizers of the congruence subgroups and also the preliminary definitions we require for discrete groups, Riemann surfaces, fundamental domains, graph theory and imprimitive action are given.

In Chapter 2, the suborbital graphs of Nor(p) are examined. It is shown that Gamma^ acts transitively and imprimitively on the set of extended rational numbers and then the number of orbit of (Gamma_0(N))^ in the set of extended rational numbers is calculated. Moreover, edge and circuit conditions on the graph arising from the action of Gamma^ on the set of extended rational numbers are determined.

Key Words: PSL(2,IR),Gamma-Modular group, Nor(p),Gamma^,(Gamma_0(N))^, Transitive permutation group,

Suborbital graph