Primitivity in torsion free cohomology Hopf algebras
We show that a connected p-compact group with a trivial center is equivalent to a product of simple p-compact groups. More generally, we show that product splittings of any connected p-compact group correspond bijectively to algebraic splittings of the fundamental group of the maximal torus as a module over the Weyl group. These are analogues for p-compact groups of well-known theorems about compact Lie groups.
Let G be a finite group. We prove that every rational G-connected Hopf G-space with two nontrivial homotopy group systems is G-homotopy equivalent to an infinite loop G-space.