Geodesic
Quasivarieties of nilpotent groups of axiomatic rank~$4$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 2131-2141

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We say that the axiomatic rank of a quasivariety $K$ is equal to $n$ if $K$ can be defined by a system of quasi-identities in $n$ variables and cannot be defined by any set of quasi-identities in fewer variables. If there is no such $n$, then $K$ has an infinite axiomatic rank. We prove that the set of quasivarieties of nilpotent torsion-free groups of class at most $2$ of axiomatic rank $4$ is continual.
Keywords: nilpotent group, quasivariety, variety, axiomatic rank. 
@article{SEMR_2020_17_a42,
     author = {A. I. Budkin},
     title = {Quasivarieties of nilpotent groups of axiomatic rank~$4$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {2131--2141},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a42/}
}
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A. I. Budkin. Quasivarieties of nilpotent groups of axiomatic rank~$4$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 2131-2141. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a42/