Asymptotic formula for sum-free sets in abelian groups

Let A be a subset of a finite abelian group G. We say that A is sum-free if there is no solution of the equation x + y = z, with x, y, z belonging to the set A. Let SF(G) denotes the set of all sum-free subets of $G$ and $\sigma (G)$ denotes the number $n^{-1}({\log }_2\mathrm{\mid }SF(G)\mathrm{\mid })$. In this article we shall improve the error term in the asymptotic formula of $\sigma (G)$ which was obtained recently by Ben Green and Ruzsa. The methods used are a slight refinement of methods developed by Ben Green and Ruzsa.