Embeddings using universal words in the free group of rank 2 (Russian version)

TL;DR

This paper presents a method for explicitly embedding any countable group into a 2-generator group, preserving certain features and enabling constructions of recursive groups within finitely presented groups.

Contribution

It introduces a specific, explicit embedding technique for countable groups into 2-generator groups, with potential applications in recursive and finitely presented groups.

Findings

Provides an explicit embedding method for countable groups

Derives defining relations for the target 2-generator group

Enables constructions of recursive groups within finitely presented groups

Abstract

For an arbitrary countable group G = <A|R> given by its generators A and defining relations R we discuss a specific method for embedding of G into a certain 2-generator group T. Our embedding explicitly lists the images of generators from A in the group T, and from the relations R it explicitly deduces defining relations for T inheriting certain special features from R. The obtained method can be used in constructions of explicit embeddings of recursive groups into finitely presented groups.