Levi classes of quasivarieties of 2-nilpotent groups

The Levi class L ( M ) generated by the class of groups M is the class of all groups in which the normal closure of each cyclic subgroup belongs to M . Let p be a prime number, p ̸ = 2 , s be a natural number, s ≥ 2 , and s > 2 for p = 3; H p s be a free group of rank 2 in the variety of nilpotent groups of class ≤ 2 of exponent p s with commutator subgroup of exponent p ; Z is an in fi nite cyclic group; q { H p s , Z } is a quasivariety generated by the set of groups { H p s , Z } . We fi nd a basis of quasi-identities of the Levi class L ( q { H p s , Z } ) and establish that there exists a continuous set of quasivarieties K such that L ( K ) = L ( q { H p s , Z } ) .