Author	Kleinert, Ernst. author
Title	Units in Skew Fields [electronic resource] / by Ernst Kleinert
Imprint	Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2000
Connect to	http://dx.doi.org/10.1007/978-3-0348-8409-9
Descript	VIII, 80 p. online resource

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

0 Basic Facts -- 1 Heyโ{128}{153}s Theorem and Consequences -- 2 Siegel-Weyl Reduction Theory -- 3 The Tamagawa Number and the Volume of G(?)/G(?) -- 3.1 Statement of the main result -- 3.2 Proof of 3.1 -- 3.3 The volume of G(?)/G(?) -- 4 The Size of ? -- 4.1 Statement of results -- 4.2 Proofs -- 5 Margulisโ{128}{153} Finiteness Theorem -- 5.1 The Result -- 5.2 Amenable groups -- 5.3 Kazhdanโ{128}{153}s property (T) -- 5.4 Proof of 5.1; beginning -- 5.5 Interlude: parabolics and their opposites -- 5.6 Continuation of the proof -- 5.7 Contracting automorphisms and the Moore Ergodicity theorem -- 5.8 End of proof -- 5.9 Appendix on measure theory -- 6 A Zariski Dense and a Free Subgroup of ? -- 7 An Example -- 8 Problems -- 8.1 Generators -- 8.2 The congruence problem -- 8.3 Betti numbers -- References