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arXiv · 1908.10665

Homogeneous completely simple semigroups

Thomas Quinn-Gregson
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Abstract

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.

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Thomas Quinn-Gregson. 2019-08-28. Homogeneous completely simple semigroups. https://arxiv.org/abs/1908.10665

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