Ünlü, Ö.Yalçın, E.2016-02-082016-02-0820120025-5874http://hdl.handle.net/11693/21529We show that every rank two p-group acts freely and smoothly on a product of two spheres. This follows from a more general construction: given a smooth action of a finite group G on a manifold M, we construct a smooth free action on M × S n1× ... × S nk when the set of isotropy subgroups of the G-action on M can be associated to a fusion system satisfying certain properties. Another consequence of this construction is that if G is an (almost) extra-special p-group of rank r, then it acts freely and smoothly on a product of r spheres. © 2011 Springer-Verlag.EnglishPrimary 57S25Secondary 20D20Article10.1007/s00209-010-0833-z1432-1823