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A new family of sofic one-relator groups.

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Title: A new family of sofic one-relator groups.
Authors: Berlai, Federico1 (AUTHOR) federico.berlai@ehu.eus
Source: International Journal of Algebra & Computation. Feb2026, Vol. 36 Issue 1, p115-120. 6p.
Subjects: Infinite groups, Mathematics, Mathematical proofs
Abstract: In this paper, we provide an infinite family of sofic one-relator groups that are not residually finite nor residually solvable. The proof is essentially different from the one in [J. P. Bannon, A non-residually solvable hyperlinear one-relator group, Proc. Amer. Math. Soc. 139(4) (2011) 1409–1410] as it does not use Magnus–Moldavanskii decompositions. [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
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Header DbId: egs
DbLabel: Engineering Source
An: 190554589
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: A new family of sofic one-relator groups.
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  Data: <searchLink fieldCode="AR" term="%22Berlai%2C+Federico%22">Berlai, Federico</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> federico.berlai@ehu.eus</i>
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Algebra+%26+Computation%22">International Journal of Algebra & Computation</searchLink>. Feb2026, Vol. 36 Issue 1, p115-120. 6p.
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  Data: In this paper, we provide an infinite family of sofic one-relator groups that are not residually finite nor residually solvable. The proof is essentially different from the one in [J. P. Bannon, A non-residually solvable hyperlinear one-relator group, Proc. Amer. Math. Soc. 139(4) (2011) 1409–1410] as it does not use Magnus–Moldavanskii decompositions. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  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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        Value: 10.1142/S0218196725500444
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      – Code: eng
        Text: English
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        PageCount: 6
        StartPage: 115
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      – SubjectFull: Infinite groups
        Type: general
      – SubjectFull: Mathematics
        Type: general
      – SubjectFull: Mathematical proofs
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              Text: Feb2026
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              Y: 2026
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