Restrictions on local embeddability into finite semigroups

TL;DR

This paper explores the properties of semigroups regarding their local embeddability into finite structures, introduces the concept of local wrapping, and characterizes certain classes of inverse semigroups.

Contribution

It extends the theory of local embeddability to semigroups, introduces local wrapping, and characterizes inverse LWF semigroups with finite idempotents.

Findings

A family of non-LEF semigroups unifies bicyclic monoid and Baumslag--Solitar groups.

Inverse LWF semigroups with finitely many idempotents are LEF.

The paper broadens understanding of local embeddability in algebraic structures.

Abstract

In this paper the concept of local embeddability into finite structures (being LEF) for the class of semigroups is expanded with investigations of non-LEF structures, a closely related generalising property of local wrapping of finite structures (being LWF) and inverse semigroups. The established results include a description of a family of non-LEF semigroups unifying the bicyclic monoid and Baumslag--Solitar groups and establishing that inverse LWF semigroups with finite number of idempotents are LEF.