  Assume M is a 3-dimensional real manifold without boundary, A is an abelian
Lie algebra of analytic vector fields on M, and X is an element of A. The
following result is proved:
  If K is a locally maximal compact set of zeroes of X and the Poincar'e-Hopf
index of X at K is nonzero, there is a point in K at which all the elements of
A vanish.
