  Let $\mathcal{W}$ be a complete local commutative Noetherian ring with
residue field $k$ of positive characteristic $p$. We study the inverse problem
for the versal deformation rings $R_{\mathcal{W}}(\Gamma,V)$ relative to
$\mathcal{W}$ of finite dimensional representations $V$ of a profinite group
$\Gamma$ over $k$. We show that for all $p$ and $n \ge 1$, the ring
$\mathcal{W}[[t]]/(p^n t,t^2)$ arises as a universal deformation ring. This
ring is not a complete intersection if $p^n\mathcal{W}\neq\{0\}$, so we obtain
an answer to a question of M. Flach in all characteristics. We also study the
`inverse inverse problem' for the ring $\mathcal{W}[[t]]/(p^n t,t^2)$; this is
to determine all pairs $(\Gamma, V)$ such that $R_{\mathcal{W}}(\Gamma,V)$ is
isomorphic to this ring.
