Variants of epigroups and primary conjugacy

Maria Borralho, Michael Kinyon

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


In a semigroup S with fixed (Formula presented.) one can construct a new semigroup (Formula presented.) called a variant by defining (Formula presented.) Elements (Formula presented.) are primarily conjugate if there exist (Formula presented.) such that (Formula presented.) This coincides with the usual conjugacy in groups, but is not transitive in general semigroups. Araújo et al. proved that transitivity holds in a variety (Formula presented.) of epigroups containing all completely regular semigroups and their variants, and asked if transitivity holds for all variants of semigroups in (Formula presented.) We answer this affirmatively as part of a study of varieties and variants of epigroups.

Original languageEnglish
Pages (from-to)5465-5473
Number of pages9
JournalCommunications in Algebra
Publication statusPublished - 2020


  • Conjugacy
  • semigroup
  • variants


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