We prove that an integral homology 3–sphere is S3 if
and only if it admits four periodic diffeomorphisms of odd prime
orders whose space of orbits is S3. As an application we
show that an irreducible integral homology sphere which is not
S3 is the cyclic branched cover of odd prime order of at
most four knots in S3. A result on the structure of finite
groups of odd order acting on integral homology spheres is also
obtained.