LEVI CLASSES OF QUASIVARIETIES OF NILPOTENT GROUPS OF EXPONENT ps

The Levi class L(M) generated by the class M of groups is the class of all groups in which the normal closure of every element belongs to M. It is proved that there exists a set of quasivarieties M of cardinality continuum such that L(M) = L(qH(ps)), where qH(ps) is the quasivariety generated by the group H-ps a free group of rank 2 in the variety R-Ps of <= 2-step nilpotent groups of exponent p(s) with commutator subgroup of exponent p, p is a prime number, p not equal 2, s is a natural number, s >= 2, and s > 2 for p = 3.