The Higman operations and embeddings of recursive groups

TL;DR

This paper introduces an algorithm utilizing Higman operations to explicitly construct recursively enumerable sets during Higman embeddings, simplifying the process for certain groups and enabling automated embeddings into 2-generator groups.

Contribution

It presents a novel algorithm that makes constructive Higman embeddings more practical and introduces auxiliary operations for easier manipulation.

Findings

Algorithm successfully constructs recursively enumerable sets during embeddings.

Simplifies the process of Higman embeddings for specific classes of groups.

Mentions an automated mechanism for embedding countable groups into 2-generator groups.

Abstract

In the context of Higman embeddings of recursive groups into finitely presented groups we suggest an algorithm which uses Higman operations to explicitly constructs the specific recursively enumerable sets of integer sequences arising during the embeddings. This makes the constructive Higman embedding a doable task for certain wide classes of groups. Specific auxiliary operations are introduced to make the work with Higman operations a simpler and more intuitive procedure. Also, an automated mechanism of constructive embeddings of countable groups into 2-generator groups is mentioned.