Groups that act pseudofreely on S2 x S2

A pseudofree group action on a space X is one whose set of singular orbits forms a discrete subset of its orbit space. Equivalently - when G is finite and X is compact - the set of singular points in X is finite. In this paper, we classify all of the finite groups which admit pseudofree actions on S-2 x S-2. The groups are exactly those that admit orthogonal pseudofree actions on S-2 x S-2 subset of R-3 x R-3, and they are explicitly listed. This paper can be viewed as a companion to a preprint of Edmonds, which uniformly treats the case in which the second Betti number of a four-manifold M is at least three.