, Volume 62, Issue 3, pp 437-442

p-Group actions on homology spheres

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When an arbitraryp-groupG acts on a ℤ n -homologyn-sphereX, it is proved here that the dimension functionn:S(G)→ℤ(S(G) is the set of subgroups ofG), defined byn(H)=dimX H, (dim here is cohomological dimension) is realised by a real representation ofG, and that there is an equivariant map fromX to the sphere of this representation. A converse is also established.