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ToolsGray, Robert (2020) Undecidability of the word problem for one-relator inverse monoids via right-angled Artin subgroups of one-relator groups. Inventiones Mathematicae, 219 (3). pp. 987-1008. ISSN 0020-9910
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Abstract
We prove the following results: (1) There is a one-relator inverse monoid Inv⟨A|w=1⟩ with undecidable word problem; and (2) There are one-relator groups with undecidable submonoid membership problem. The second of these results is proved by showing that for any finite forest the associated right-angled Artin group embeds into a one-relator group. Combining this with a result of Lohrey and Steinberg (J Algebra 320(2):728–755, 2008), we use this to prove that there is a one-relator group containing a fixed finitely generated submonoid in which the membership problem is undecidable. To prove (1) a new construction is introduced which uses the one-relator group and submonoid in which membership is undecidable from (2) to construct a one-relator inverse monoid Inv⟨A|w=1⟩ with undecidable word problem. Furthermore, this method allows the construction of an E-unitary one-relator inverse monoid of this form with undecidable word problem. The results in this paper answer a problem originally posed by Margolis et al. (in: Semigroups and their applications, Reidel, Dordrecht, pp. 99–110, 1987).
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | 20f05,20f10,20f36,20m05,20m18,free-products,identity problem |
| Faculty \ School: | Faculty of Science > School of Mathematics (former - to 2024) |
| UEA Research Groups: | Faculty of Science > Research Groups > Algebra and Combinatorics (former - to 2024) Faculty of Science > Research Groups > Algebra, Logic & Number Theory |
| Related URLs: | |
| Depositing User: | LivePure Connector |
| Date Deposited: | 09 Sep 2019 15:30 |
| Last Modified: | 07 Nov 2024 12:41 |
| URI: | https://ueaeprints.uea.ac.uk/id/eprint/72132 |
| DOI: | 10.1007/s00222-019-00920-2 |
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