  The study of separating invariants is a recent trend in invariant theory. For
a finite group acting linearly on a vector space, a separating set is a set of
invariants whose elements separate the orbits of G. In some ways, separating
sets often exhibit better behavior than generating sets for the ring of
invariants. We investigate the least possible cardinality of a separating set
for a given G-action. Our main result is a lower bound that generalizes the
classical result of Serre that if the ring of invariants is polynomial then the
group action must be generated by pseudoreflections. We find these bounds to be
sharp in a wide range of examples.
