Units in Skew Fields

This book is devoted to a study of the unit groups of orders in skew fields, finite dimensional and central over the rational field; it thereby belongs to the field of noncommutative arithmetic. Its purpose is a synopsis of results and methods, including full proofs of the most important results. It is addressed to researchers in number theory and arithmetic groups. Front Matter....Pages i-viii Basic Facts....Pages 1-4 Hey’s Theorem and Consequences....Pages 5-7 Siegel-Weyl Reduction Theory....Pages 8-16 The Tamagawa Number and the Volume of G (R)/ G (Z)....Pages 17-30 The Size of Г....Pages 31-40 Margulis’ Finiteness Theorem....Pages 41-59 A Zariski Dense and a Free Subgroup of Г....Pages 60-65 An Example....Pages 66-71 Problems....Pages 72-76 Back Matter....Pages 77-80