  In this paper we prove two new results about closed semigroups in the family
of solvable groups H_{mn} that are semidirect products of R^m and R^n, and for
which the structure homomorphism maps nontrivially into the center of Aut(R^n).
The first result states that the closure of a semigroup generated by a set in
H_{mn} that is not included in a maximal semigroup with nonempty interior is
actually a group. The second result states that among the subsets of H_{mn}
that are not included in a maximal proper semigroup, those that generate H_{mn}
as a closed semigroup are dense. Results of this nature were obtained before
only for extensions of nilpotent groups. Results of this nature were obtained
before only for abelian and nilpotent Lie groups and their compact extensions.
As an application of the technique developed in the paper, we find the minimal
number of generators as a closed group and as a closed semigroup of H_{mn}.
