The Axiomatic Rank of the Levi Class Generated by the Almost Abelian Quasivariety of Nilpotent Groups

Abstract

Let $$\mathcal{M}$$ be a quasivariety generated by a relatively free group in a class of nilpotent groups of step $$\leq 2$$ with commutator subgroups of prime exponent $$p,$$ $$p\neq 2.$$ A class $$L(\mathcal{M})$$ of all groups $$G$$ the normal closure of any element in which belongs to $$\mathcal{M}$$ is called the Levi class generated by $$\mathcal{M}.$$ It is proved that $$L(\mathcal{M})$$ has finite axiomatic rank, i.e., $$L(\mathcal{M})$$ can be defined by a system of quasi-identities with a finite number of variables.