On groups with EDT0L word problem.
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| Title: | On groups with EDT0L word problem. |
|---|---|
| Authors: | Bishop, Alex1 (AUTHOR) alexbishop1234@gmail.com, Elder, Murray2 (AUTHOR) murray.elder@uts.edu.au, Evetts, Alex3 (AUTHOR) aevetts@hotmail.co.uk, Gallot, Paul4 (AUTHOR) pgallot@uni-bremen.de, Levine, Alex5 (AUTHOR) a.levine@uea.ac.uk |
| Source: | International Journal of Algebra & Computation. Jun2026, Vol. 36 Issue 4, p425-486. 62p. |
| Subjects: | Group theory, Infinite groups, Formal languages, Generators of groups, Finite groups |
| Abstract: | We prove that the word problem for the infinite cyclic group is not EDT0L, and obtain as a corollary that a finitely generated group with EDT0L word problem must be torsion. In addition, we show that the property of having an EDT0L word problem is invariant under change of generating set, and passing to finitely generated subgroups. This represents significant progress toward the conjecture that all groups with EDT0L word problem are finite (i.e. precisely the groups with regular word problem). [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal of Algebra & Computation is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 193893251 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: On groups with EDT0L word problem. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Bishop%2C+Alex%22">Bishop, Alex</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> alexbishop1234@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Elder%2C+Murray%22">Elder, Murray</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> murray.elder@uts.edu.au</i><br /><searchLink fieldCode="AR" term="%22Evetts%2C+Alex%22">Evetts, Alex</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> aevetts@hotmail.co.uk</i><br /><searchLink fieldCode="AR" term="%22Gallot%2C+Paul%22">Gallot, Paul</searchLink><relatesTo>4</relatesTo> (AUTHOR)<i> pgallot@uni-bremen.de</i><br /><searchLink fieldCode="AR" term="%22Levine%2C+Alex%22">Levine, Alex</searchLink><relatesTo>5</relatesTo> (AUTHOR)<i> a.levine@uea.ac.uk</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Algebra+%26+Computation%22">International Journal of Algebra & Computation</searchLink>. Jun2026, Vol. 36 Issue 4, p425-486. 62p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Group+theory%22">Group theory</searchLink><br /><searchLink fieldCode="DE" term="%22Infinite+groups%22">Infinite groups</searchLink><br /><searchLink fieldCode="DE" term="%22Formal+languages%22">Formal languages</searchLink><br /><searchLink fieldCode="DE" term="%22Generators+of+groups%22">Generators of groups</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+groups%22">Finite groups</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We prove that the word problem for the infinite cyclic group is not EDT0L, and obtain as a corollary that a finitely generated group with EDT0L word problem must be torsion. In addition, we show that the property of having an EDT0L word problem is invariant under change of generating set, and passing to finitely generated subgroups. This represents significant progress toward the conjecture that all groups with EDT0L word problem are finite (i.e. precisely the groups with regular word problem). [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal of Algebra & Computation is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1142/S0218196726500165 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 62 StartPage: 425 Subjects: – SubjectFull: Group theory Type: general – SubjectFull: Infinite groups Type: general – SubjectFull: Formal languages Type: general – SubjectFull: Generators of groups Type: general – SubjectFull: Finite groups Type: general Titles: – TitleFull: On groups with EDT0L word problem. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Bishop, Alex – PersonEntity: Name: NameFull: Elder, Murray – PersonEntity: Name: NameFull: Evetts, Alex – PersonEntity: Name: NameFull: Gallot, Paul – PersonEntity: Name: NameFull: Levine, Alex IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 02181967 Numbering: – Type: volume Value: 36 – Type: issue Value: 4 Titles: – TitleFull: International Journal of Algebra & Computation Type: main |
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