  We consider the preservation under products, finite powers, and forcing, of a
selection principle based covering property of $T_0$ topological groups. Though
the paper is in part a survey, it contributes some new information, including:
  1. The product of a strictly o-bounded group with an o-bounded group is an
o-bounded group - Corollary 18
  2. In the generic extension by a finite support iteration of $\aleph_1$
Hechler reals the product of any o-bounded group with a ground model $\aleph_0$
bounded group is an o-bounded group - Theorem 19
  3. In the generic extension by a countable support iteration of length
$\aleph_2$ Mathias reals the product of any o-bounded group with a ground model
$\aleph_0$ bounded group is an o-bounded group - Theorem 20.
