  The rank of a semigroup is the cardinality of a smallest generating set. In
this paper we compute the rank of the endomorphism monoid of a non-trivial
uniform partition of a finite set, that is, the semigroup of those
transformations of a finite set that leave a non-trivial uniform partition
invariant. That involves proving that the rank of a wreath product of two
symmetric groups is two and then use the fact that the endomorphism monoid of a
partition is isomorphic to a wreath product of two full transformation
semigroups. The calculation of the rank of these semigroups solves an open
question.
