Abelianness and centrality in inverse semigroups

TL;DR

This paper extends the concepts of abelianness and centrality from universal algebra to inverse semigroups, providing characterizations and linking centrality to conjugation, and shows that certain classes of inverse semigroups are actually groups.

Contribution

It introduces a novel adaptation of abelianness and centrality concepts to inverse semigroups and characterizes these properties via congruence pairs.

Findings

Abelian and central congruences characterized in inverse semigroups.

Centrality related to conjugation in inverse semigroups.

Solvable and nilpotent inverse semigroups are groups.

Abstract

We adapt the abstract concepts of abelianness and centrality of universal algebra to the context of inverse semigroups. We characterize abelian and central congruences in terms of the corresponding congruence pairs. We relate centrality to conjugation in inverse semigroups. Subsequently we prove that solvable and nilpotent inverse semigroups are groups.