The objective of this work is to establish bounded generation for two families of Sarithmetic groups. We first establish bounded generation for the special linear group over certain S-orders of a quaternion algebra. We also establish bounded generation for certain special unitary groups.This thesis consists of three chapters. The first chapter provides much of the background necessary as well as providing some applications of bounded generation.
This paper uses the methods from [2] to give 'short' presentations for Aut + (Fn), the special automorphism group of the free group of rank n, and Out + (Fn) the special outer automorphism group of the free group of rank n.
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