  In this paper, we prove by means of a counterexample that there exist pair of
integers (n,p) with $n\geq 3$, $2\leq p\leq n-1$, and open sets $D$ in $C^{n}$
which are cohomologically $p$-complete with respect to the structure sheaf of
$D$ such that the cohomology group $H_{n+p}(D,Z)$ does not vanish. In
particular $D$ is not $p$-complete.
