Undecidability of the submonoid membership problem for free nilpotent group of class $l\geqslant 2$ of sufficiently large rank Full article
| Journal |
Izvestiya Mathematics
ISSN: 1064-5632 |
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| Output data | Year: 2023, Volume: 87, Number: 4, Pages: 798-816 Pages count : 19 DOI: 10.4213/im9342e | ||
| Tags | submonoid membership problem, nilpotent group, Hilbert’s tenth problem, interpretability of equations in groups | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Омский филиал ФГБУН «Институт математики им. С.Л. Соболева СО РАН». | FWNF-2022-0003 |
Abstract:
An answer is given to the question of M. Lohrey and B. Steinberg on decidability of the submonoid membership problem for a finitely generated nilpotent group. Namely, a finitely generated submonoid of a free nilpotent group of class 2 of sufficiently large rank r is constructed, for which the membership problem is algorithmically undecidable. This implies the existence of a submonoid with similar property in any free nilpotent group of class l ⩾ 2 of rank r. The proof is based on the undecidability of Hilbert’s tenth problem.
Cite:
Roman'kov V.A.
Undecidability of the submonoid membership problem for free nilpotent group of class $l\geqslant 2$ of sufficiently large rank
Izvestiya Mathematics. 2023. V.87. N4. P.798-816. DOI: 10.4213/im9342e WOS Scopus РИНЦ OpenAlex
Undecidability of the submonoid membership problem for free nilpotent group of class $l\geqslant 2$ of sufficiently large rank
Izvestiya Mathematics. 2023. V.87. N4. P.798-816. DOI: 10.4213/im9342e WOS Scopus РИНЦ OpenAlex
Original:
Романьков В.А.
Неразрешимость проблемы вхождения в подмоноид свободной нильпотентной группы ступени l≥2 достаточно большого ранга
Известия Российской академии наук. Серия математическая. 2023. Т.87. №4. С.166–185. DOI: 10.4213/im9342 РИНЦ OpenAlex
Неразрешимость проблемы вхождения в подмоноид свободной нильпотентной группы ступени l≥2 достаточно большого ранга
Известия Российской академии наук. Серия математическая. 2023. Т.87. №4. С.166–185. DOI: 10.4213/im9342 РИНЦ OpenAlex
Dates:
| Submitted: | Mar 22, 2023 |
| Published print: | Oct 23, 2023 |
| Published online: | Oct 23, 2023 |
Identifiers:
| Web of science: | WOS:001088986700005 |
| Scopus: | 2-s2.0-85174948971 |
| Elibrary: | 63568626 |
| OpenAlex: | W4387757270 |