The Levi classes generated by nilpotent groups. (Q542190)

Let \(M\) be an arbitrary class of groups. Denote by \(L(M)\) the class of all groups \(G\) in which the normal closure \((x)^G\) of every element \(x\) of \(G\) belongs to \(M\). The class \(L(M)\) is called the Levi class generated by \(M\). It is known that if \(M\) is a variety of groups then so is \(L(M)\); if \(M\) is a quasivariety of groups then so is \(L(M)\). By \(qF_p\) the author denotes the quasivariety generated by the relatively free group in the class of nilpotent groups of length at most 2 with the commutant of exponent \(p\) (where \(p\) is an odd prime). The author describes the Levi class that is generated by \(qF_p\).