Geodesic
On the $\omega $-independence of quasivarieties of nilpotence groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 516-522

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We prove that there exists a set $\mathcal{R}$ of quasivarieties of nilpotent groups of class two any quasivariety from $\mathcal{R} $ does not have an independent basis of quasi-identities to the class $\mathcal{N}_{2}$ of $2$-nilpotent groups and has an $\omega $-independent basis of quasi-identities to $\mathcal{N}_{2}$. The intersection of all quasivarieties in $\mathcal{R}$ has an independent basis of quasi-identities to $\mathcal{N}_{2}$. The set of such sets $\mathcal{R}$ is continual.
Keywords: nilpotent group, quasivariety, $\omega $-independence. 
@article{SEMR_2019_16_a7,
     author = {A. I. Budkin},
     title = {On the $\omega $-independence of quasivarieties of nilpotence groups},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {516--522},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a7/}
}
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A. I. Budkin. On the $\omega $-independence of quasivarieties of nilpotence groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 516-522. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a7/