Higman operations on integer sequences, and embeddings of recursive groups

TL;DR

This paper explores the use of Higman operations on integer sequences to analyze the embeddings of various recursive groups into finitely presented groups, advancing understanding of their structural relationships.

Contribution

It introduces new methods for embedding recursive groups into finitely presented groups using Higman operations on integer sequences.

Findings

Established explicit embedding techniques for recursive groups

Demonstrated the applicability of Higman operations in group embeddings

Extended previous results on group embeddings and presentations

Abstract

This is an extended version of summary of the talk at the International Conference on Group Theory in honor of Victor Mazurov on the occasion of his 80th birthday. The concise version of this report can be found in the talks and communications band at the Conference site. The objective of the current talk is to present our very recent article in which we for various types of recursive groups discuss possibility of their explicit embeddings into finitely presented groups.