Sum-free sets in abelian groups

We show that there is an absolute constant delta > 0 such that the number o f sum-free subsets of any finite abelian group G is (2(nu (G)) - 1) 2(\G\/2) + O(2((1/2 - delta)\G\)). where nu (G) is the number of even order components in the canonical decomp osition of G into a direct sum of its cyclic subgroups, and the implicit co nstant in the O-sign is absolute.