Kernels of restriction maps in the mod-p cohomology of p-groups
V\~o Thanh T\`ung

Abstract. Let $p$ be a prime number. The purpose of this paper is to
investigate kernels of restriction maps in mod-$p$ cohomology of 
$p$-groups. This result is applied to prove that, if $K$ is a $2$-group
which is not elementary abelian, and if $\xi,\xi_1,\dots,\xi_r,\dots$
is a sequence of mod-$2$ cohomology classes of $K$ which restrict 
trivially to all proper subgroups, then $Sq^{n-r}(\xi)\cdot\xi_0\cdot
\xi_1\cdot\dots\cdot\xi_r=0$ where $n=\deg(\xi)$ and $\xi_0=1$.