Subvariety structures in certain product varieties of groups

Mikaelian, Vahagn H.

doi:10.1515/jgth-2018-0017

Cited by 5 publications

(1 citation statement)

References 22 publications

(36 reference statements)

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“…In particular, we do prove the part "These two conditions are easy, but a little tedious, to check, and this is left to the reader" on p. 472 in [11], and we do give a proof for Lemma 2.2 mentioned in [11] as "obvious from the normal form theorem". In fact, we could shorten the proofs even more by evolving some of our wreath product methods [14]- [17]. However, we intentionally keep technique within free products with amalgamations and HNN-extensions to preserve Higman's original idea of investigation of recursion via free constructions.…”

Section: Comparison Of the Current Modification Withmentioning

confidence: 99%

A modified proof for Higman's embedding theorem

Mikaelian¹

2019

Preprint

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We suggest a modified and briefer version for the proof of Higman's embedding theorem stating that a finitely generated group can be embedded in a finitely presented group if and only if it is recursively presented. In particular, we shorten the main part of original proof establishing characterization of recursive relations in terms of benign subgroups in free groups. Also, some technical lemmas on homomorphisms in free constructions are replaced by simple combinatorial observations on words of specific type."We do fundamental research, not only to acquire results solely, but because the process is an ennobling one"

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Section: Comparison Of the Current Modification Withmentioning

confidence: 99%

A modified proof for Higman's embedding theorem

Mikaelian¹

2019

Preprint

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Embeddings Determined by Universal Words in the Rank 2 Free Group

Mikaelian

2021

Sib Math J

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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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Subvariety structures in certain product varieties of groups

Cited by 5 publications

References 22 publications

A modified proof for Higman's embedding theorem

A modified proof for Higman's embedding theorem

Embeddings Determined by Universal Words in the Rank 2 Free Group

The Higman operations and embeddings of recursive groups

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