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This article is cited in 1 scientific paper (total in 1 paper)
Levi classes of quasivarieties of nilpotent groups of exponent $p^s$
V. V. Lodeishchikovaa, S. A. Shakhovab a Altai State University, Barnaul
b Altai State University, Barnaul
Abstract:
The Levi class $L(\mathcal{M})$ generated by the class $\mathcal{M}$ of groups is the class of all groups in which the normal closure of every element belongs to $\mathcal{M}$. It is proved that there exists a set of quasivarieties $\mathcal{M}$ of cardinality continuum such that $L(\mathcal{M})=L(qH_{p^{s}})$, where $qH_{p^{s}}$ is the quasivariety generated by the group $H_{p^{s}}$, a free group of rank $2$ in the variety $\mathcal{R}^{p^{s}}$ of $\leq 2$-step nilpotent groups of exponent $p^{s}$ with commutator subgroup of exponent $p$, $p$ is a prime number, $p\neq 2$, $s$ is a natural number, $s\geq 2$, and $s>2$ for $p=3$.
Keywords:
quasivariety, Levi class, nilpotent group.
Received: 21.01.2022 Revised: 07.06.2022
Citation:
V. V. Lodeishchikova, S. A. Shakhova, “Levi classes of quasivarieties of nilpotent groups of exponent $p^s$”, Algebra Logika, 61:1 (2022), 77–92
Linking options:
https://www.mathnet.ru/eng/al2697 https://www.mathnet.ru/eng/al/v61/i1/p77
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Abstract page: | 112 | Full-text PDF : | 41 | References: | 31 | First page: | 3 |
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