The mod 2 semicharacteristic and groups acting freely on manifolds (Q2266489)

The author, by making use of the equivariant fixed point theorem which he established [Jap. J. Math., New Ser. 4, 263-298 (1978; Zbl 0404.57028)], proves some results on groups acting freely on closed \((2n+1)\)- dimensional or closed orientable \((4n+1)\)-dimensional topological manifolds. In the last case, he proves: (1) If the group is a 2-group and the mod 2 semicharacteristic of the manifold is non-null, then the group is cyclic. (2) If the group is finite with trivial action on the cohomology ring of the manifold and the manifold has mod 2 semicharacteristic non-null, then the group is the direct product of a cyclic 2-group and a group of odd order.