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On groups of units of special and one-relator inverse monoids
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dc.contributor.author | Gray, Robert D. | |
dc.contributor.author | Ruskuc, Nik | |
dc.date.accessioned | 2023-11-22T16:30:07Z | |
dc.date.available | 2023-11-22T16:30:07Z | |
dc.date.issued | 2023-11-21 | |
dc.identifier | 294266584 | |
dc.identifier | 19618d7f-82ec-4067-a0c6-31ea5f9b72c4 | |
dc.identifier | 85178227632 | |
dc.identifier.citation | Gray , R D & Ruskuc , N 2023 , ' On groups of units of special and one-relator inverse monoids ' , Journal of the Institute of Mathematics of Jussieu , vol. FirstView . https://doi.org/10.1017/S1474748023000439 | en |
dc.identifier.issn | 1474-7480 | |
dc.identifier.other | ORCID: /0000-0003-2415-9334/work/147472861 | |
dc.identifier.uri | https://hdl.handle.net/10023/28750 | |
dc.description | Funding: This research of R. D. Gray was supported by the Engineering and Physical Sciences Research Council projects EP/N033353/1 “Special inverse monoids: subgroups, structure, geometry, rewriting systems and the word problem”, and EP/V032003/1 ‘’Algorithmic, topological and geometric aspects of infinite groups, monoids and inverse semigroups”. | en |
dc.description.abstract | We investigate the groups of units of one-relator and special inverse monoids. These are inverse monoids which are defined by presentations, where all the defining relations are of the form r=1. We develop new approaches for finding presentations for the group of units of a special inverse monoid, and apply these methods to give conditions under which the group admits a presentation with the same number of defining relations as the monoid. In particular, our results give sufficient conditions for the group of units of a one-relator inverse monoid to be a one-relator group. When these conditions are satisfied, these results give inverse semigroup theoretic analogues of classical results of Adjan for one-relator monoids, and Makanin for special monoids. In contrast, we show that in general these classical results do not hold for one-relator and special inverse monoids. In particular, we show that there exists a one-relator special inverse monoid whose group of units is not a one-relator group (with respect to any generating set), and we show that there exists a finitely presented special inverse monoid whose group of units is not finitely presented. | |
dc.format.extent | 44 | |
dc.format.extent | 438973 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of the Institute of Mathematics of Jussieu | en |
dc.subject | One-relator monoid | en |
dc.subject | One-relator group | en |
dc.subject | Inverse monoid | en |
dc.subject | Special inverse monoid | en |
dc.subject | Units | en |
dc.subject | Right units | en |
dc.subject | Coherence | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | On groups of units of special and one-relator inverse monoids | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | https://doi.org/10.1017/S1474748023000439 | |
dc.description.status | Peer reviewed | en |
dc.identifier.url | https://arxiv.org/abs/2103.02995 | en |
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