On the $\omega$-independence of quasivarieties of nilpotence groups

Abstract

We prove that there exists a set R of quasivarieties of nilpotent groups of class two any quasivariety from R does not have an independent basis of quasi-identities to the class N2 of 2-nilpotent groups and has an ω-independent basis of quasi-identities to N2. The intersection of all quasivarieties in R has an independent basis of quasiidentities to N2. The set of such sets R is continual.