  Suppose that G is a discrete abelian group and A is a finite symmetric subset
of G. We show two main results. i) Either there is a set H of O(log^c|A|)
subgroups of G with |A \triangle \bigcup H| = o(|A|), or there is a character X
on G such that -wh{1_A}(X) >> log^c|A|. ii) If G is finite and |A|>> |G| then
either there is a subgroup H of G such that |A \triangle H| = o(|A|), or there
is a character X on G such that -wh{1_A}(X)>> |A|^c.
