We study homology
3-spheres M that admit fixed point free actions by a finite group G. If G also admits
a fixed point free orthogonal action on S3 and if certain projective Z[G]-modules
satisfy a cancellation property we show that the regular covering M→M∕G is
induced from a standard regular covering S3→ S3∕G by means of a map
f :M∕G → S3∕G whose degree is relatively prime to the order of G (Theorem 1). We
also completely characterize those regular coverings M→ M where M is Seifert
fibered (§4). Finally, starting with any given regular covering M0→ M0 with
group of covering transformations G, M0 irreducible, and M0 a homology
3-sphere, we show how to construct another regular covering M→ M with M a
homology 3-sphere and the same group G of covering transformations, with M
sufficiently large, M and M0 not homotopy equivalent, and a degree 1 map
f : M → M0 that induces the regular covering M→ M from the regular covering
M0→ M0.
