  A semigroup is completely simple if it has no proper ideals and contains a
primitive idempotent. We say that a completely simple semigroup $S$ is a
homogeneous completely simple semigroup if any isomorphism between finitely
generated completely simple subsemigroups of $S$ extends to an automorphism of
$S$. Motivated by the study of homogeneous completely regular semigroups, we
obtain a complete classification of homogeneous completely simple semigroups,
modulo the group case. As a consequence, all finite regular homogeneous
semigroups are described, thus extending the work of Cherlin on homogeneous
finite groups.
