Title: The index of compact simple Lie groups,
Abstract: Let M be an irreducible Riemannian symmetric space. The index i(M) of M is
the minimal codimension of a (non-trivial) totally geodesic submanifold of M.
The purpose of this note is to determine the index i(M) for all irreducible
Riemannian symmetric spaces M of type (II) and (IV).