Commutators in Completely Simple Semigroups
Jelena Radović, Nebojša Mudrinski · arXiv (Cornell University) · 2022
We obtain a characterization of the binary commutator on completely simple semigroups, using their Rees matrix representation. Consequently, we prove that a regular semigroup is nilpotent (solvable) if and only if it is simple, and all its $\mathcal{H}$-classes are nilpotent (solvable) groups.