  For each odd prime p, we exhibit p-groups G of p-rank two such that (suitably
defined) Chern classes of unitary representations of G fail to generate the
following rings:
  1. The even degree integral cohomology of G;
  2. The final page of the Atiyah-Hirzebruch spectral sequence for G;
  3. The Brown-Peterson generalized cohomology of G.
  It follows that these groups afford counterexamples to conjectures of C. B.
Thomas, M. F. Atiyah and P. Landweber.
