Conjugacy in inverse semigroups

João Araújo, Michael Kinyon, Janusz Konieczny

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)142-173
Number of pages32
JournalJournal of Algebra
Volume533
DOIs
Publication statusPublished - 1 Sep 2019

Keywords

  • Bicyclic monoid
  • Clifford semigroups
  • Conjugacy
  • Factorizable inverse monoids
  • Free inverse semigroups
  • Inverse semigroups
  • McAllister P-semigroups
  • Stable inverse semigroups
  • Symmetric inverse semigroups

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