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A Levi Class Generated by a Quasivariety of Nilpotent Groups

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Algebra and Logic Aims and scope

Let L(M) be a class of all groups G in which the normal closure of any element belongs to M; qM is a quasivariety generated by a class M. We consider a quasivariety qH2 generated by a relatively free group in a class of nilpotent groups of class at most 2 with commutator subgroup of exponent 2. It is proved that the Levi class L(qH2) generated by the quasivariety qH2 is contained in the variety of nilpotent groups of class at most 3.

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  1. Polzunov Altai State Technical University, pr. Lenina 46, Barnaul, 656038, Russia

    V. V. Lodeishchikova

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  1. V. V. Lodeishchikova
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Correspondence to V. V. Lodeishchikova.

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Translated from Algebra i Logika, Vol. 58, No. 4, pp. 486-499, July-August, 2019.

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Lodeishchikova, V.V. A Levi Class Generated by a Quasivariety of Nilpotent Groups. Algebra Logic 58, 327–336 (2019). https://doi.org/10.1007/s10469-019-09554-y

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  • DOI: https://doi.org/10.1007/s10469-019-09554-y

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