The Higman operations and embeddings of recursive groups

Abstract

In the context of Higman embeddings for 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 embedding. This makes the constructive Higman embedding a doable task for certain classes of groups. Specific auxiliary operations are introduced to make the work with of Higman operations a simpler and more intuitive procedure. Also, an automated mechanism of constructive embedding of countable groups into 2-generator groups is mentioned.