On isomorphisms to a free group and beyond

2023/09/07 by Vladimir Shpilrain, Shpilrain, Vladimir
Computer Science · Mathematics · #20F10 #Advanced Graph Theory Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2309.03819

openalex publication_date 2023/09/07 · openalex created_date 2023/09/09 · openalex updated_date 2026/07/28

Abstract

The isomorphism problem for infinite finitely presented groups is probably the hardest among standard algorithmic problems in group theory. Classes of groups where it has been completely solved are nilpotent groups, hyperbolic groups, and limit groups. In this short paper, we address the problem of isomorphism to particular groups, including free groups. We also address the algorithmic problem of embedding a finitely presented group in a given limit group.

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