  Let V be a compact Kahler manifold. Let G' be a commutative subgroup of
Aut(V) and U the set of elements of zero entropy of G'. Then U is a group and
G' is isomorphic to the direct product of groups U and G where G is a subgroup
of G' such that all elements of G, except the identity, are of positive
entropy. Moreover, G is a free commutative group with rank(G)<dim(V). The
estimate is sharp. When rank(G)=dim(V)-1, U is finite. Rank(G) satisfies other
inequalities involving the dimensions of Dolbeault cohomology groups of V.
