  A real Milnor manifold is the non-singular hypersurface of degree $(1,1)$ in
the product of two real projective spaces. These manifolds were introduced by
Milnor to give generators for the unoriented cobordism algebra, and they admit
free actions by elementary abelian 2-groups. In this paper, we obtain some
results on the free 2-rank of symmetry of products of finitely many real Milnor
manifolds under the assumption that the induced action on mod 2 cohomology is
trivial. Similar results are obtained for complex Milnor manifolds which are
defined analogously. Here the free 2-rank of symmetry of a topological space is
the maximal rank of an elementary abelian 2-group which acts freely on that
space.
