TY - JOUR
T1 - Conjugacy in inverse semigroups
AU - Araújo, João
AU - Kinyon, Michael
AU - Konieczny, Janusz
N1 - info:eu-repo/grantAgreement/FCT/5876/147271/PT#
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.
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 -