A well known conjecture in the theory of transformation groups states that if
p is a prime and (Z/p)^r acts freely on a product of k spheres, then r is less
than or equal to k. We prove this assertion if p is large compared to the
dimension of the product of spheres. The argument builds on tame homotopy
theory for non simply connected spaces.Comment: 30 pages; improved exposition, some details adde