Some examples in the integral and Brown-Peterson cohomology of $p$-groups

Ian J. Leary and Nobuaki Yagita 

Abstract  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.  

Bull. London Math. Soc. 24 (1992), 165-168.