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arXiv · 1902.03822

Undecidability of the word problem for one-relator inverse monoids via right-angled Artin subgroups of one-relator groups

Robert D. Gray
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Abstract

We prove the following results: (1) There is a one-relator inverse monoid $\mathrm{Inv}\langle A\:|\:w=1 \rangle$ with undecidable word problem; and (2) There are one-relator groups with undecidable submonoid membership problem. The first of these results answers a problem originally posed by Margolis, Meakin and Stephen in 1987.

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Robert D. Gray. 2019-02-11. Undecidability of the word problem for one-relator inverse monoids via right-angled Artin subgroups of one-relator groups. https://doi.org/10.1007/s00222-019-00920-2

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