Semivarieties of nilpotent groups

Semivarieties of groups are quasivarieties defined by quasi-identities of the form $t=1\to f=1$. It is proved that a set of semivarieties in every variety of class two nilpotent $p$-groups of finite exponent having a commutator subgroup of exponent $p$ ($p$ is a prime) is at most countable. It is stated that a variety of class two nilpotent groups with commutator subgroup of exponent $p$ contains a set of semivarieties of the cardinality of the continuum.