THEOREM 7. IfK is reducible to L and K' to L', then K 0 L is reducible to K' 0 L'. THEOREM 8. For a direct sum I1 + 112 of abelian groups H1 and II2, A0(H11 + II2) is reducible to A0(1) 0 A0(II2). Together with Theorem 2 and the results for cyclic groups, these Theorems prove THEOREM 9. If 11 is a finitely generated abelian group, then any abelian homology or cohomology group A,(II) or Af(II, J...

1. Background. The subject of this address is a branch of mathematics which may be regarded as a combination of the classical theory of representations of finite groups by matrices and that part of analysis centering around the theory of Fourier series and integrals. The connection between these two apparently diverse subjects arises simply enough from the fact that the real numbers and the rea...

We give some new characterizations of exactness for locally compact second countable groups. In particular, we prove that a locally compact group is exact if and only if it admits a topologically amenable action on a compact Hausdorff space. This answers an open question by Anantharaman-Delaroche.