Sum-free sets in abelian groups

We show that there is an absolute constant δ>0 such that the number of sum-free subsets of any finite abelian groupG is\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\left( {2^{\nu (G)} - 1} \right)2^{\left| G \right|/2} + O\left( {2^{(1/2 - \delta )\left| G \right|} } \right)$$ \end{document} whereν(G) is the number of even order components in the canonical decomposition ofG into a direct sum of its cyclic subgroups, and the implicit constant in theO-sign is absolute.