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Sibirskii Matematicheskii Zhurnal, 2024, Volume 65, Number 4, Pages 727–734
DOI: https://doi.org/10.33048/smzh.2024.65.411 (Mi smj7887) 		 
Algebraic closures in divisible rigid groups

N. S. Romanovskii

Novosibirsk State University
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DOI: https://doi.org/10.33048/smzh.2024.65.411
Abstract: We prove that in a divisible $m$-rigid group the algebraic closure of each set generating a subgroup of solvability length $m$ coincides with the elementary closure of this set.
Keywords: group, solvable group, elementary theory, algebraic closure.
Funding agency Grant number
Russian Science Foundation 24-21-00214
The work was supported by the Russian Science Foundation (Grant no. 24–21–00214, https://rscf.ru/project/24-21-00214/).
Received: 01.02.2024
Revised: 01.02.2024
Accepted: 20.06.2024
English version:
Siberian Mathematical Journal, 2024, Volume 65, Issue 4, Pages 840–845
DOI: https://doi.org/10.1134/S0037446624040116
Document Type: Article
UDC: 512.5+510.6
MSC: 35R30
Language: Russian
Citation: N. S. Romanovskii, “Algebraic closures in divisible rigid groups”, Sibirsk. Mat. Zh., 65:4 (2024), 727–734; Siberian Math. J., 65:4 (2024), 840–845
Citation in format AMSBIB
\Bibitem{Rom24}
\by N.~S.~Romanovskii
\paper Algebraic closures in divisible rigid groups
\jour Sibirsk. Mat. Zh.
\yr 2024
\vol 65
\issue 4
\pages 727--734
\mathnet{http://mi.mathnet.ru/smj7887}
\transl
\jour Siberian Math. J.
\yr 2024
\vol 65
\issue 4
\pages 840--845
\crossref{https://doi.org/10.1134/S0037446624040116}
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