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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. The second chapter contains the proof of bounded generation for some special linear groups, and the third chapter contains the proof of bounded generation for some special unitary groups.

Bounded Generation of Two Families of S-Arithmetic Groups