Quasivarieties of nilpotent groups of axiomatic rank 4. (English) Zbl 1454.20058
Summary: 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.
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