The Higman operations and embeddings of recursive groups

Author:

Mikaelian Vahagn H.1ORCID

Affiliation:

1. Informatics & Applied Mathematics Department , Yerevan State University , Alex Manoogian 1 , Yerevan 0025 , Armenia

Abstract

Abstract In the context of Higman embeddings of recursive groups into finitely presented groups, we suggest an approach, termed the 𝐻-machine, which for certain wide classes of groups allows constructive Higman embeddings of recursive groups into finitely presented groups. The approach is based on Higman operations, and it explicitly constructs some specific recursively enumerable sets of integer sequences arising during the embeddings. 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 preserving certain “patterns” is mentioned.

Funder

Ministry of Education and Science

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

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