A modified proof for Higman's embedding theorem

2019/08/27 by Vahagn H. Mikaelian, Mikaelian, V. H. · 1 citation
Computer Science · Mathematics · #20D15 #20E10 #20E22 #20K01 #20K25 #Computability, Logic, AI Algorithms #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1908.10153

openalex publication_date 2019/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 are replaced by simple combinatorial observations on words in free constructions.

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

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