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ToolsDolinka, Igor and Gray, Robert (2021) New results on the prefix membership problem for one-relator groups. Transactions of the American Mathematical Society, 374 (6). pp. 4309-4358. ISSN 0002-9947
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Abstract
In this paper we prove several results regarding decidability ofthe membership problem for certain submonoids in amalgamated free prod-ucts and HNN extensions of groups. These general results are then appliedto solve the prefix membership problem for a number of classes of one-relatorgroups which are low in the Magnus–Moldavanski ̆ı hierarchy. Since the pre-fix membership problem for one-relator groups is intimately related to theword problem for one-relator special inverse monoids in theE-unitary case(as discovered in 2001 by Ivanov, Margolis and Meakin), these results yieldsolutions of the word problem for several new classes of one-relator specialinverse monoids. In establishing these results, we introduce a new theory ofconservative factorisations of words which provides a link between the pre-fix membership problem of a one-relator group and the group of units of thecorresponding one-relator special inverse monoid. Finally, we exhibit the firstexample of a one-relator group, defined by a reduced relator word, that has anundecidable prefix membership problem.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | one-relator group,prefix membership problem,special inverse monoid,word problem,mathematics(all),applied mathematics ,/dk/atira/pure/subjectarea/asjc/2600 |
| 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, Number Theory, Logic, and Representations (ANTLR) |
| Related URLs: | |
| Depositing User: | LivePure Connector |
| Date Deposited: | 10 Nov 2020 01:17 |
| Last Modified: | 13 Dec 2024 01:30 |
| URI: | https://ueaeprints.uea.ac.uk/id/eprint/77601 |
| DOI: | 10.1090/tran/8338 |
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