Z/p x Z/p actions on Sn x Sn

We determine the homotopy type of quotients of S(n )x S-n by free actions of Z(/p) x Z(/p) where 2p > n + 3 . Much like free Z(/p) actions, they can be classified via the first p -localized k -invariant, but there are restrictions on the possibilities, and these restrictions are sufficient to determine every possibility in the n = 3 case. We use this to complete the classification of free Z(/p) x Z(/p) actions on S(3 )x S-3 for p > 3 by reducing the problem to the simultaneous classification of pairs of binary quadratic forms. Although the restrictions are not sufficient to determine which k-invariants are realizable in general, they can sometimes be used to rule out free actions by groups that contain Z(/p) x Z(/p) as a normal abelian subgroup.