We continue to study quasivarieties of groups closed underdirect Z-wreath products.We show that such quasivarieties contain finitelygenerated groups which are not finitely defined in every quasivariety ofgroups. We establish the existence of continuum many finitely generatedgroups every of which is not finitely defined in each quasivariety ofgroups. We construct the group which is finitely defined in the classof all torsion-free groups and is not finitely defined in the class of allgroups.
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