  We prove a Smith-type inequality for regular covering spaces in monopole
Floer homology. Using the monopole Floer / Heegaard Floer correspondence, we
deduce that if a 3-manifold Y admits a p^n-sheeted regular cover that is a
Z/pZ-L-space (for p prime), then Y is a Z/pZ-L-space. Further, we obtain
constraints on surgeries on a knot being regular covers over other surgeries on
the same knot, and over surgeries on other knots.
