  A 3-coloring of the elements of an abelian group is said to be rainbow--free
if there is no 3-term arithmetic progression with its members having pairwise
distinct colors. We give a structural characterization of rainbow--free
colorings of abelian groups. This characterization proves a conjecture of
Jungi\'c et al. on the size of the smallest chromatic class of a rainbow-free
3-coloring of cyclic groups.
