The Finite Embedding Property for IP Loops and Local Embeddability of Groups into Finite IP Loops

TL;DR

This paper proves that all inverse property loops have the Finite Embedding Property, enabling groups to be locally embedded into finite IP loops, expanding understanding of loop structures and their relation to groups.

Contribution

It establishes the Finite Embedding Property for IP loops and shows that groups can be locally embedded into finite IP loops, a novel connection between groups and loop theory.

Findings

IP loops have the Finite Embedding Property

Groups are locally embeddable into finite IP loops

Advances understanding of the structure of IP loops

Abstract

We prove that the class of all loops with the inverse property (IP loops) has the Finite Embedding Property (FEP). As a consequence, every group is locally embeddable into finite IP loops.