  The known manifolds of positive sectional curvature are either homogeneous
spaces or biquotients, i.e. quotients of a compact Lie group by a group acting
on the left and right simultaneously. The full isometry group of the
homogeneous metrics of positive curvature were determined by K.Shankar. Here we
determine the isometry group of some of the biquotients due to Eschenburg and
Bazaikin. As an application we obtain, as in the homogeneous case, more
counterexamples to the Chern conjecture, which states that an abelian subgroup
of the fundamental group of a positively curved manifold is cyclic.
