Embeddings Determined by Universal Words in the Rank 2 Free Group

Mikaelian, Vahagn H.

doi:10.1134/s0037446621010134

Sib Math J

2021

DOI: 10.1134/s0037446621010134

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Embeddings Determined by Universal Words in the Rank 2 Free Group

Vahagn H. Mikaelian

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The Higman operations and embeddings of recursive groups

Mikaelian

2023

Journal of Group Theory

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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.

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The Higman operations and embeddings of recursive groups

Mikaelian

2023

Journal of Group Theory

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On Benign Subgroups Constructed by Higman’s Sequence Building Operation

Atabekyan,

Mikaelian

2024

J. Contemp. Mathemat. Anal.

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Embeddings Determined by Universal Words in the Rank 2 Free Group

Cited by 2 publications

References 16 publications

The Higman operations and embeddings of recursive groups

The Higman operations and embeddings of recursive groups

On Benign Subgroups Constructed by Higman’s Sequence Building Operation

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