20.18 (2022)

Let $\mathfrak{R}_{p^k}$ be the variety of class 2 nilpotent groups of exponent $p^k$, where $p$ is a prime number and $k \geqslant 2$. It is true that for every $p$ and $k$ there are infinitely many subquasivarieties of $\mathfrak{R}_{p^k}$ each of which is generated by a finite group with derived subgroup of exponent $p^k$ and does not have an independent basis of quasi-identities?