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arXiv · 2605.00041

The Inverse Monoid of Partial Inner Automorphisms of a Semigroup

João Araújo·Wolfram Bentz·Michael Kinyon·Janusz Konieczny António Malheiro·Valentin Mercier
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Abstract

We introduce the inverse monoid of inner partial automorphisms of a semigroup -- a tool that associates to every semigroup an inverse semigroup. When the semigroup is a group, this inverse semigroup is isomorphic to the group of inner automorphisms with a zero adjoined. We then describe this structure for completely simple semigroups, the full transformation monoid, and the endomorphism monoid of a finite $G$-set when $G$ is a finite abelian group. The paper ends with some open problems.

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João Araújo, Wolfram Bentz, Michael Kinyon, Janusz Konieczny António Malheiro, Valentin Mercier. 2026-04-28. The Inverse Monoid of Partial Inner Automorphisms of a Semigroup. https://arxiv.org/abs/2605.00041

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