Giordano, Thierry,Booth, Andrew L.2009-03-192009-03-1919981998Source: Masters Abstracts International, Volume: 37-04, page: 1221.9780612366657http://hdl.handle.net/10393/4073http://dx.doi.org/10.20381/ruor-13563In 1955, Henry Dye showed that factors with isomorphic unitary groups are in a certain sense isomorphic, provided they are not of type $I\sb{2n}.$ We establish a similar result for simple AF algebras, namely that the unitary group of a simple AF algebra is a complete invariant. Also, there appears to be an error in Dye's paper which allows us to strengthen his result so that it is valid for factors not of type $I\sb2.$144 p.Mathematics.Thesis