Abstract
Let \( L_{n}({\mathcal{N}}) \) be the class of all groups \( G \) in which the normal closure of each \( n \)-generated subgroup of \( G \) belongs to \( {\mathcal{N}} \). It is known that if \( {\mathcal{N}} \) is a quasivariety of groups then so is \( L_{n}({\mathcal{N}}) \). We find the conditions on \( {\mathcal{N}} \) for the sequence \( L_{1}({\mathcal{N}}),L_{2}({\mathcal{N}}),\dots \) to contain infinitely many different quasivarieties. In particular, such are the quasivarieties \( {\mathcal{N}} \) generated by a finitely generated nilpotent nonabelian group.
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04 December 2023
A typo in the pagination of the original Russian paper is corrected in the HTML and PDF versions.
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Acknowledgments
The author expresses his gratitude to Svetlana Shakhova and Victoriya Lodeishchikova for discussions and a careful reading of the article.
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Translated from Sibirskii Matematicheskii Zhurnal, 2023, Vol. 64, No. 4, pp. 733–741. https://doi.org/10.33048/smzh.2023.64.406
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Budkin, A.I. Groups with Nilpotent \( n \)-Generated Normal Subgroups. Sib Math J 64, 847–853 (2023). https://doi.org/10.1134/S0037446623040067
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DOI: https://doi.org/10.1134/S0037446623040067