The Levi class L(M) generated by the class M of groups is the class of all groups in which the normal closure of every element belongs to M. It is proved that there exists a set of quasivarieties M of cardinality continuum such that \( L\left(\mathrm{M}\right)=L\left(q{H}_{p^s}\right) \), where \( q{H}_{p^s} \) is the quasivariety generated by the group \( {H}_{p^s} \), a free group of rank 2 in the variety \( {R}^{p^s} \) of ≤ 2-step nilpotent groups of exponent ps with commutator subgroup of exponent p, p is a prime number, p ≠ 2, s is a natural number, s ≥ 2, and s > 2 for p = 3.
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Translated from Algebra i Logika, Vol. 61, No. 1, pp. 77-92, January-February, 2022. Russian DOI: https://doi.org/10.33048/alglog.2022.61.104.
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Lodeishchikova, V.V., Shakhova, S.A. Levi Classes of Quasivarieties of Nilpotent Groups of Exponent ps. Algebra Logic 61, 54–66 (2022). https://doi.org/10.1007/s10469-022-09674-y
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DOI: https://doi.org/10.1007/s10469-022-09674-y