Non-linear Group Actions with Polynomial Invariant Rings and a Structure Theorem for Modular Galois Extensions

Peter Fleischmann, Chris Woodcock

Let $G$ be a finite $p$-group and $k$ a field of characteristic $p>0$. We show that $G$ has a \emph{non-linear} faithful action on a polynomial ring $U$ of dimension $n=\mathrm{log…