We consider discrete, Zariski-dense subgroups of a real Lie group G
which contain a lattice inside the unipotent radical of a parabolic
subgroup of G. For most simple Lie groups G of real rank greater than
1, it was proven by Hee Oh that such a discrete subgroup is always an
arithmetic lattice. For G a rank 1 group such as SL(2,R), this is not
always the case. We take G to be a product of Lie groups of real rank
1 (this was originally investigated by Selberg when G is a product of
SL2's), then, under a suitable condition, all such discrete subgroups
are again arithmetic. We'll give a proof of this when G is a product
of orthogonal groups of rank 1.