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

Fixed point data of finite groups acting on 3–manifolds