A Levi Class Generated by a Quasivariety of Nilpotent Groups

Abstract

Let L(M) be a class of all groups G in which the normal closure of any element belongs to M; qM is a quasivariety generated by a class M. We consider a quasivariety qH₂ generated by a relatively free group in a class of nilpotent groups of class at most 2 with commutator subgroup of exponent 2. It is proved that the Levi class L(qH₂) generated by the quasivariety qH₂ is contained in the variety of nilpotent groups of class at most 3.