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Algebra Logika, 2020, Volume 59, Number 6, Pages 719–733 (Mi al2644)  

Communications

Two problems for solvable and nilpotent groups

V. A. Roman'kovab

a Siberian Federal University, Krasnoyarsk, Russia
b Sobolev Institute of Mathematics, Omsk

Abstract: Section 1 gives a brief review of known results on embeddings of solvable, nilpotent, and polycyclic groups in $2$-generated groups from these classes, including the description of the author's recently obtained solution to the Mikaelian–Ol'schanskii problem on embeddings of finitely generated solvable groups of derived length $l$ in solvable groups of derived length $l+1$ with a fixed small number of generators.
Section 2 contains a somewhat more extensive review of known results on the rational subset membership problem for groups, including the presentation of the author's recently obtained solution to the Laurie–Steinberg–Kambites–Silva–Zetsche problem of whether the membership problem is decidable for finitely generated submonoids of free nilpotent groups.

Funding Agency Grant Number
Russian Science Foundation 19-71-10017
Supported by Russian Science Foundation, project No. 19-71-10017.


DOI: https://doi.org/10.33048/alglog.2020.59.606

Full text: PDF file (241 kB)
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English version:
Algebra and Logic, 2021, 59:6, 483–492

Bibliographic databases:

UDC: 512.54
Received: 10.12.2020
Revised: 05.03.2021

Citation: V. A. Roman'kov, “Two problems for solvable and nilpotent groups”, Algebra Logika, 59:6 (2020), 719–733; Algebra and Logic, 59:6 (2021), 483–492

Citation in format AMSBIB
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\paper Two problems for solvable and nilpotent groups
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\vol 59
\issue 6
\pages 719--733
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\pages 483--492
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