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This article is cited in 2 scientific papers (total in 2 papers)
Mathematical logic, algebra and number theory
Quasivarieties of nilpotent groups of axiomatic rank $4$
A. I. Budkin Altai State University, 61, Lenina ave., Barnaul, 656049, Russia
Abstract:
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.
Received April 16, 2020, published December 22, 2020
Citation:
A. I. Budkin, “Quasivarieties of nilpotent groups of axiomatic rank $4$”, Sib. Èlektron. Mat. Izv., 17 (2020), 2131–2141
Linking options:
https://www.mathnet.ru/eng/semr1337 https://www.mathnet.ru/eng/semr/v17/p2131
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Abstract page: | 175 | Full-text PDF : | 68 | References: | 31 |
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