The Atiyah conjecture for a discrete group G states that the L-Betti numbers of a finite CW-complex with fundamental group G are integers if G is torsion-free, and in general that they are rational numbers with denominators determined by the finite subgroups of G. Here we establish conditions under which the Atiyah conjecture for a torsion-free group G implies the Atiyah conjecture for every fi...
