Ph.D. Tezi Görüntüleme | |||||||||||||||||||||
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| Summary: In this thesis, the main subject is to find some invariants of the signature of the normalizer N_PSL(2,R)(Gamma_0(N)) by using suborbital graphs.In Chapter 1, the structure of Non-Euclidean Crystallographic groups is discussed and some properties of PSL(2,R), 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 N_PSL(2,R)(Gamma_0(N)) and number of orbits of Gamma_0(N) in are examined. Edge and circuit conditions on graphs arising from the action of Gamma_0(N) on are determined. And , as the core of the thesis are found necessary and sufficient conditions for the suborbital graph F_(u,N) to be a forest. That is, it is shown that F_(u,N) is a forest if and only if it contains no n-gon , circuits of length n.Key Words: PSL(2,R), Gamma, Gamma_0(N), N_PSL(2,R)(Gamma_0(N)), Transitive Permutation Group, Suborbital Graph, Geodesic , Index
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