  In this paper we develop the theory of homogeneous functions between finite
abelian groups. Here, a function $f:G\longrightarrow H$ between finite abelian
groups is homogeneous of degree $d$ if $f(nx)=n^df(x)$ for all $x\in G$ and all
$n$ which are relatively prime to the order of $x$. We show that the group of
homogeneous functions of degree one from a group $G$ of odd order to
$\mathbb{Q}/\mathbb{Z}$ maps onto $SK_1(\mathbb{Z}[G])$, generalizing a result
of R. Oliver for $p$-groups.
