Non-Abelian extensions of degree $p^3$ and $p^4$ in characteristic $p>2$

Abstract

This paper describes in terms of Artin-Schreier equations field extensions whose Galois group is isomorphic to any of the four non-cyclic groups of order $p^3$ or the ten non-Abelian groups of order $p^4$, $p$ an odd prime, over a field of characteristic $p$.