A Counterexample to the mod-p version of the \bar{Ch}-conjecture
for any odd prime p.

Pham Anh Minh
Department of Mathematics
College of Sciences
University of Hue
Dai hoc Khoa hoc
Hue
Vietnam

Abstract.

The $\bar{Ch}$-conjecture states that, for every $p$-group $G$ ($p$ odd),
$H^*(G,\mathbb F_p)/\sqrt{0}$ is generated by Chern classes of unitary
representations of $G$ and images under transfers from proper subgroups
of $G$. It was known that, for $p = 3$, the extraspecial $p$-group of order
$27$ and exponent $3$ was a counterexample to that conjecture. We now 
provide counterexample to that conjecture for any odd prime $p$.