  A point $P$ in projective space is said to be Galois with respect to a
hypersurface if the function field extension induced by the projection from $P$
is Galois. We present a hyperplane section theorem for Galois points.
Precisely, if $P$ is a Galois point for a hypersurface, then $P$ is Galois for
a general hyperplane section passing through $P$. As an application, we
determine hypersurfaces of dimension $n$ with $n$-dimensional sets of Galois
points.

Algebraic Geometry