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Two Problems for Solvable and Nilpotent Groups

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Algebra and Logic Aims and scope

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.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Omsk, Russia

    V. A. Roman’kov

  2. Siberian Federal University, Krasnoyarsk, Russia

    V. A. Roman’kov

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  1. V. A. Roman’kov
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Correspondence to V. A. Roman’kov.

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Translated from Algebra i Logika, Vol. 59, No. 6, pp. 719-733, November-December, 2020. Russian DOI: https://doi.org/10.33048/alglog.2020.59.606.

Supported by Russian Science Foundation, project No. 19-71-10017.

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Roman’kov, V.A. Two Problems for Solvable and Nilpotent Groups. Algebra Logic 59, 483–492 (2021). https://doi.org/10.1007/s10469-021-09617-z

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  • DOI: https://doi.org/10.1007/s10469-021-09617-z

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