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math.GR2026
The Inverse Monoid of Partial Inner Automorphisms of a Semigroup
João Araújo, Wolfram Bentz, Michael Kinyon +2
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…
math.GR2026
Conjugacy in Abstract Semigroups, Transformation and Diagram Monoids, and Conjugacy Growth
João Araújo, Wolfram Bentz, Michael Kinyon +3
We study conjugacy relations on semigroups and monoids, focusing on the relation $a \cfn b$, defined by the existence of such that , , , an…