The Vagner-Preston representation of a block-group

TL;DR

This paper extends the Vagner-Preston representation to block-groups and identifies its kernel as the largest congruence separating regular elements, advancing the algebraic understanding of these structures.

Contribution

It introduces a novel extension of the Vagner-Preston representation specifically for block-groups, highlighting its kernel's role in separating regular elements.

Findings

Extended Vagner-Preston representation for block-groups.

Identified the kernel as the largest congruence separating regular elements.

Provides new algebraic insights into block-group structures.

Abstract

In this short note we construct an extension of the Vagner-Preston representation for block-groups and show that its kernel is the largest congruence that separates regular elements.