  R. S. Kulkarni showed that a finite group acting pseudofreely, but not
freely, preserving orientation, on an even-dimensional sphere (or suitable
sphere-like space) is either a periodic group acting semifreely with two fixed
points, a dihedral group acting with three singular orbits, or one of the
polyhedral groups, occurring only in dimension 2. It is shown here that the
dihedral group does not act pseudofreely and locally linearly on an actual
n-sphere when n is congruent to 0 mod 4. The possibility of such an action when
n is congruent to 2 mod 4 and n>2 remains open. Orientation-reversing actions
are also considered.
