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

2020/09/22 by Vahagn H. Mikaelian, Mikaelian, V. H. · 1 citation
Computer Science · Mathematics · #20D15 #20E10 #20E22 #20K01 #20K25 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2009.10571

openalex publication_date 2020/09/22 · openalex created_date 2020/10/01 · openalex updated_date 2026/07/28

Abstract

For an arbitrary countable group G = 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.

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• Explicit construction of benign subgroup for Higman's reversing operation

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