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.

中文翻译：

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同质完全简单的半群

如果一个半群没有合适的理想并且包含一个原始幂等，那么它是完全简单的。如果$S$ 的有限生成完全简单子半群之间的同构扩展到$S$ 的自同构，我们就说完全简单半群$S$ 是齐次完全简单半群。受齐次完全正则半群研究的启发，我们得到齐次完全简单半群的完整分类，以群情况为模。因此，描述了所有有限正则齐次半群，从而扩展了 Cherlin 在齐次有限群上的工作。