Special subgroups of regular semigroups

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Extending the notions of inverse transversal and associate subgroup, we consider a regular semigroup S with the property that there exists a subsemigroup T which contains, for each x∈S, a unique y such that both xy and yx are idempotent. Such a subsemigroup is necessarily a group which we call a special subgroup. Here, we investigate regular semigroups with this property. In particular, we determine when the subset of perfect elements is a subsemigroup and describe its structure in naturally arising situations.

Original languageEnglish
Pages (from-to)4246-4256
Number of pages11
JournalCommunications in Algebra
Issue number10
Publication statusPublished - 3 Oct 2017


  • Quasi-ideal
  • regular semigroup
  • special subgroup


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