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// Sibirskii Matematicheskii Zhurnal
// Archive
Sibirsk. Mat. Zh.,
2024
Volume 65,
Number 4,
Pages
727–734
(Mi smj7887)
Algebraic closures in divisible rigid groups
N. S. Romanovskii
Novosibirsk State University
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.
UDC:
512.5+
510.6
MSC:
35R30
Received:
01.02.2024
Revised:
01.02.2024
Accepted:
20.06.2024
DOI:
10.33048/smzh.2024.65.411
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References
©
Steklov Math. Inst. of RAS
, 2024