A semigroup S is called a \(\varDelta \)-semigroup if the lattice of its congruences forms a chain relative to the inclusion. A local automorphism of a semigroup S is defined as an isomorphism between its two subsemigroups. The set of all local automorphisms of a semigroup S relative to the operation of composition forms an inverse monoid of local automorphisms. We present a classification of all finite semigroups for which the inverse monoid of local automorphisms is a \(\varDelta \)-semigroup.

中文翻译：

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有限半群的完全分类，其局部自同构的逆单等式为$$ \ varDelta $$Δ-半群

如果半群S的全等格相对于包含物形成一条链，则称为\（\ varDelta \） -半群。半群S的局部自同构被定义为其两个亚半群之间的同构。相对于合成操作，半群S的所有局部自同构的集合形成了局部自同构的逆单半体。我们给出了所有有限半群的分类，对于这些半群，局部自同构的逆半体像是\（\ varDelta \）-半群。