TY - JOUR

T1 - Conjugacy in inverse semigroups

AU - Araújo, João

AU - Kinyon, Michael

AU - Konieczny, Janusz

N1 - The 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, and CEMAT project UID/Multi/04621/2013.
The second author was also partially supported by a Simons Foundation Collaboration Grant 359872.

PY - 2019/9/1

Y1 - 2019/9/1

N2 - 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.

AB - 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.

KW - Bicyclic monoid

KW - Clifford semigroups

KW - Conjugacy

KW - Factorizable inverse monoids

KW - Free inverse semigroups

KW - Inverse semigroups

KW - McAllister P-semigroups

KW - Stable inverse semigroups

KW - Symmetric inverse semigroups

UR - http://www.scopus.com/inward/record.url?scp=85067242288&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2019.05.022

DO - 10.1016/j.jalgebra.2019.05.022

M3 - Article

AN - SCOPUS:85067242288

VL - 533

SP - 142

EP - 173

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -