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Sibirskii Matematicheskii Zhurnal, 2025, Volume 66, Number 2, Pages 213–218
DOI: https://doi.org/10.33048/smzh.2025.66.207 (Mi smj7939) 		 
One question of the theory of numbered groups

N. Kh. Kasymov

Mirzo Ulugbek National University, Tashkent, Uzbekistan
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DOI: https://doi.org/10.33048/smzh.2025.66.207
Abstract: We show that the kernel of every numbered group is a permutation computable equivalence. We also prove the existence of a permutation computable equivalence over which no group is definable.
Keywords: numbered group, definability of a group over equivalence, permutation computable equivalence.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2024-1438
The author is supported by the development program of the Scientific and Education Mathematical Center of Kazan (Volga Region) Federal University (Agreement 075–02–2024–1438).
Received: 15.08.2024
Revised: 28.01.2025
Accepted: 25.02.2025
English version:
Siberian Mathematical Journal, 2025, Volume 66, Issue 2, Pages 298–302
DOI: https://doi.org/10.1134/S0037446625020077
Document Type: Article
UDC: 510.5
MSC: 35R30
Language: Russian
Citation: N. Kh. Kasymov, “One question of the theory of numbered groups”, Sibirsk. Mat. Zh., 66:2 (2025), 213–218; Siberian Math. J., 66:2 (2025), 298–302
Citation in format AMSBIB
\Bibitem{Kas25}
\by N.~Kh.~Kasymov
\paper One question of the theory of numbered groups
\jour Sibirsk. Mat. Zh.
\yr 2025
\vol 66
\issue 2
\pages 213--218
\mathnet{http://mi.mathnet.ru/smj7939}
\transl
\jour Siberian Math. J.
\yr 2025
\vol 66
\issue 2
\pages 298--302
\crossref{https://doi.org/10.1134/S0037446625020077}
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