  This paper contributes to the study of sets of finite intrinsic perimeter in
Carnot groups. Our intent is to characterize in which groups the only sets with
constant intrinsic normal are the vertical half-spaces. Our viewpoint is
algebraic: such a phenomenon happens if and only if the semigroup generated by
each horizontal half-space is a vertical half-space. We call
\emph{semigenerated} those Carnot groups with this property.
  For Carnot groups of nilpotency step 3 we provide a complete characterization
of semigeneration in terms of whether such groups do not have any Engel-type
quotients. Engel-type groups, which are introduced here, are the minimal (in
terms of quotients) counterexamples.
  In addition, we give some sufficient criteria for semigeneration of Carnot
groups of arbitrary step. For doing this, we define a new class of Carnot
groups, which we call type $(\Diamond)$ and which generalizes the previous
notion of type $(\star)$ defined by M. Marchi. As an application, we get that
in type $ (\Diamond) $ groups and in step 3 groups that do not have any
Engel-type algebra as a quotient, one achieves a strong rectifiability result
for sets of finite perimeter in the sense of Franchi, Serapioni, and
Serra-Cassano.
