  We show that certain subrings of the cohomology of a finite p-group P may be
realised as the images of restriction from suitable virtually free groups. We
deduce that the cohomology of P is a finite module for any such subring.
Examples include the ring of `universally stable elements' defined by Evens and
Priddy, and rings of invariants such as the mod-2 Dickson algebras.
