Robert D. Gray

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20242026

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4 papers · 1 filter

math.GR2026

The word problem for two-generator one-relator inverse monoids

Robert D. Gray, Catherine Reilly

We study the word problem in two-generator one-relator inverse monoids, proving both decidability and undecidability results. We give the first example of a two-generator one-relat…

math.GR2026

The Diophantine problem in the Baumslag-Gersten group

Robert D. Gray, Alex Levine

We show that, for every positive prime number $p$ , the Baumslag-Gersten group $G_{p} = ⟨ a, t ∣ (t a t^{- 1}) a (t a t^{- 1})^{- 1} = a^{p} ⟩$ has an undecidable Diophantine pro…

math.GR2026

Finite complete rewriting systems for graphs of free groups with applications to free-by-cyclic, one-relator, and three-manifold groups

Robert D. Gray, Marco Linton

We prove that any finite graph of finitely generated free groups admits a finite complete rewriting system after possibly taking a free product with a free group of rank two. As a…

math.GR2026

Undecidable Diophantine problems in generalisations of one-relator groups

Robert D. Gray, Alex Levine

Motivated by the open problem of whether all one-relator groups have decidable Diophantine problem, in this paper we prove a collection of undecidability results about the Diophant…