Loop conditions

TL;DR

This paper classifies simple algebraic conditions called loop conditions, represented by graphs, and identifies the Siggers term as the weakest non-trivial example, advancing understanding of algebraic structures.

Contribution

It provides a classification of loop conditions with undirected graphs and establishes the Siggers term as the minimal non-trivial condition.

Findings

Classification of loop conditions with undirected graphs

Identification of the Siggers term as the weakest non-trivial condition

Framework for analyzing algebraic conditions via graph representations

Abstract

We discuss such Maltsev conditions that consist of just one linear equation, we call them loop conditions. To every such condition can be assigned a graph. We provide a classification of conditions with undirected graphs. It follows that the Siggers term is the weakest non-trivial loop condition.