Araújo, JoãoKinyon, MichaelKonieczny, Janusz2020-12-112020-12-112019-09-010021-8693PURE: 18784027PURE UUID: 115f835e-5812-454e-8cfc-54c32b1f4916Scopus: 85067242288WOS: 000474332500007http://hdl.handle.net/10362/108473The first and second authors were partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/2019 (Centro de Matematica e Aplicacoes), the project PTDC/MHC-FIL/2583/2014, the FCT project PTDC/MAT-PUR/31174/2017. The second author was also partially supported by a Simons Foundation Collaboration Grant 359872.In a group G, elements a and b are conjugate if there exists g∈G such that g−1ag=b. This conjugacy relation, which plays an important role in group theory, can be extended in a natural way to inverse semigroups: for elements a and b in an inverse semigroup S, a is conjugate to b, which we will write as a∼ib, if there exists g∈S1 such that g−1ag=b and gbg−1=a. The purpose of this paper is to study the conjugacy ∼i in several classes of inverse semigroups: symmetric inverse semigroups, McAllister P-semigroups, factorizable inverse monoids, Clifford semigroups, the bicyclic monoid, stable inverse semigroups, and free inverse semigroups.32534440engBicyclic monoidClifford semigroupsConjugacyFactorizable inverse monoidsFree inverse semigroupsInverse semigroupsMcAllister P-semigroupsStable inverse semigroupsSymmetric inverse semigroupsAlgebra and Number Theoryjournal article10.1016/j.jalgebra.2019.05.022https://www.scopus.com/pages/publications/85067242288