  In this contribution to the study of one dimensional point potentials, we
prove that if we take the limit $q\to 0$ on a potential of the type
$v_0\delta({y})+{2}v_1\delta'({y})+w_0\delta({y}-q)+ {2} w_1\delta'({y}-q)$, we
obtain a new point potential of the type ${u_0} \delta({y})+{2 u_1}
\delta'({y})$, when $ u_0$ and $ u_1$ are related to $v_0$, $v_1$, $w_0$ and
$w_1$ by a law having the structure of a group. This is the Borel subgroup of
$SL_2({\mathbb R})$. We also obtain the non-abelian addition law from the
scattering data. The spectra of the Hamiltonian in the exceptional cases
emerging in the study are also described in full detail. It is shown that for
the $v_1=\pm 1$, $w_1=\pm 1$ values of the $\delta^\prime$ couplings the
singular Kurasov matrices become equivalent to Dirichlet at one side of the
point interaction and Robin boundary conditions at the other side.
