Unstable modules over the Steenrod algebra and cohomology of groups

Hans-Werner Henn

To appear in Proc Symp Pure Math (proceedings, Seattle conference)


\begin{abstract}
Let $p$ be a prime. In this survey we attempt to 
explain how the presence of Steenrod operations in the mod - $p$ cohomology 
ring $H^*(G;\FF_p)$ of a group $G$ allows to understand qualitative features 
of this ring, at least for a large class of groups including all finite 
groups but also many discrete groups like arithmetic groups, mapping class 
groups and automorphism groups of free groups. We will also discuss how 
the general theory can be applied to do actual calculations.
\end{abstract}