  The paper deals with a problem of Additive Combinatorics. Let ${\mathbf G}$
be a finite abelian group of order $N$. We prove that the number of subset
triples $A,B,C\subset {\mathbf G}$ such that for any $x\in A$, $y\in B$ and
$z\in C$ one has $x+y\ne z$ equals $$
  3\cdot 4^N+N3^{N+1} + O((3-c_*)^N) $$ for some absolute constant $c_*>0$.
This provides a tight estimate for the number of independent sets in a special
3-uniform linear hypergraph and gives a support for the natural conjecture
concerning the maximal possible number of independent sets in such hypergraphs
on $n$ vertices.
