The restriction map in cohomology of finite 2-groups (Q1173894)

For a finite 2-group \(G\) the author considers the ideal \(\text{Ess}(G)\) of the \(\text{mod }2\) cohomology ring of \(G\), consisting of the elements which, for all proper subgroups of \(G\), restrict to zero. It follows from a celebrated result of Quillen that \(\text{Ess}(G)\) is nilpotent. It is shown that for many 2-groups the nilpotency degree \(\text{hil}(G)\) of \(\text{Ess}(G)\) is 1 or 2. It is not known whether there are groups with \(\text{hil}(G)\geq 3\).