Date

2014

Department or Program

Mathematics

Primary Wellesley Thesis Advisor

Stanley Chang

Abstract

The modular group PSL(2,Z) is well known to be the group of linear fractional transformations of the upper half of the complex plane. It is isomorphic to the quotient SL(2,Z)/K of the special linear group by its center K = {-I, I}. It acts on the hyperbolic plane as a discrete subgroup of PSL(2,R). Our work concerns the identification of quotients of PSL(2,Z) by the normal subgroups N(g) generated by a single element g. We will demonstrate great variation in the quotient types depending on the parity of the length of generating word, and apply these differences through evaluating the Cayley diagrams of these quotient groups. We will also develop an understanding of these N(g) by the action of PSL(2, Z) and its quotient groups on H, the upper half-plane model of hyperbolic space.

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