Finite isometry groups of 4-manifolds with positive sectional curvature

Let M be an oriented compact Riemannian 4-manifold with positive sectional curvature. Let G be a finite subgroup of the isometry group of M. We prove that, if G is a finite group of order , then

(i)	G is isomorphic to a subgroup of PU(3) if |G| is odd;
(ii)	G contains an index at most 2 normal subgroup which is isomorphic to a subgroup of SO(5) or PU(3) if |G| is even, and M is not homeomorphic to S 4.

Moreover, M is homeomorphic to if G is non-abelian of odd order. Supported partially by NSF Grant 19925104 of China, 973 project of Foundation Science of China and the Max-Planck Institut für Mathematik at Bonn.