  This paper gives the cohomology classification of finitistic spaces X
equipped with free actions of the group G = S3 and the orbit space X/G is the
integral or mod 2 cohomology quaternion projective space HPn. We have proved
that X is the integral or mod 2 cohomology (4n+3)-sphere or the product of
3-sphere and quaternion projective space HPn.
  Similar results for G = S1 actions are also discussed.
