Finite semigroups that are minimal for not being Malcev nilpotent

TL;DR

This paper characterizes finite semigroups that are minimal with respect to not being Malcev nilpotent, meaning all their proper substructures are Malcev nilpotent but the semigroup itself is not.

Contribution

It provides a detailed description of finite semigroups that are minimal non-Malcev nilpotent, extending the understanding from groups to semigroups.

Findings

Characterization of minimal non-Malcev nilpotent finite semigroups

Extension of known group results to semigroups

Identification of structural properties of such semigroups

Abstract

We give a description of finite semigroups $S$ that are minimal for not being Malcev nilpotent, i.e. every proper subsemigroup and every proper Rees factor semigroup is Malcev nilpotent but $S$ is not. For groups this question was considered by Schmidt.