Relative Maltsev Definability of some Commutator Properties

TL;DR

This paper demonstrates that in varieties with a Taylor term, multiple commutator properties can be characterized using Maltsev conditions, linking algebraic properties with definability criteria.

Contribution

It establishes the definability of certain commutator properties via Maltsev conditions within Taylor varieties, advancing the understanding of algebraic structure characterization.

Findings

Commutator properties are definable by Maltsev conditions in Taylor varieties.

Provides a framework connecting commutator properties with Maltsev conditions.

Enhances algebraic classification methods for varieties with Taylor terms.

Abstract

We show that, when restricted to the class of varieties that have a Taylor term, several commutator properties are definable by Maltsev conditions.