Bounded Generation of Two Families of S-Arithmetic Groups

Author:
Heald, Andrea, Mathematics - Graduate School of Arts and Sciences, University of Virginia
Advisor:
Rapinchuk, Andrei, Department of Mathematics, University of Virginia
Abstract:

The objective of this work is to establish bounded generation for two families of S- arithmetic 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.

Degree:
PHD (Doctor of Philosophy)
Keywords:
Bounded Generation, Arithmetic Groups
Language:
English
Rights:
All rights reserved (no additional license for public reuse)
Issued Date:
2013/06/07