  We consider fully effective orientation-preserving smooth actions of a given
finite group G on smooth, closed, oriented 3-manifolds M. We investigate the
relations that necessarily hold between the numbers of fixed points of various
non-cyclic subgroups. In Section 2, we show that all such relations are in fact
equations mod 2, and we explain how the number of independent equations yields
information concerning low-dimensional equivariant cobordism groups. Moreover,
we restate a theorem of A. Szucs asserting that under the conditions imposed on
a smooth action of G on M as above, the number of G-orbits of points x in M
with non-cyclic stabilizer G_x is even, and we prove the result by using
arguments of G. Moussong. In Sections 3 and 4, we determine all the equations
for non-cyclic subgroups G of SO(3).
