  In this paper we show that most rank two groups act freely on a finite
homotopy product of two spheres. This makes new progress on a conjecture by
Benson and Carlson which states that a finite group G acts freely on a finite
complex with the homotopy type of n spheres if the rank of G is less than or
equal to n. Recalling that Qd(p) is the semidirect product of a rank two
elementary abelian p-group with SL(2,p), we show that a rank two finite group
acts freely on a finite CW-complex homotopic to the product of two spheres if,
it does not contain any subquotient isomorphic to Qd(p) for any odd prime p.
