  Steinberg showed that when a finite reflection group acts on a real or
complex vector space of finite dimension, the Jacobian determinant of a set of
basic invariants factors into linear forms which define the reflecting
hyperplanes. This result generalizes verbatim to fields whose characteristic is
prime to the order of the group. Our main theorem gives a generalization of
Steinberg's result for arbitrary fields using a ramification formula of Benson
and Crawley-Boevey. As an intermediate result, we show that every finite group
which fixes a hyperplane pointwise has a polynomial ring of invariants.
