This analysis characterizes abelian and central congruences in inverse semigroups, highlighting their relations to groups.
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.
No takes yet. Share an insight, caveat, or question.
Kinyon et al. (2025) studied this question.
Synapse has enriched one closely related paper. Consider it for comparative context: