9.4 (1984)

It is known that if $\mathfrak{M}$ is a variety (quasivariety, pseudovariety) of groups, then the class $I\mathfrak{M}$ of all quasigroups that are isotopic to groups in $\mathfrak{M}$ is also a variety (quasivariety, pseudovariety), and $I\mathfrak{M}$ is finitely based if and only if $\mathfrak{M}$ is finitely based. Is it true that if $\mathfrak{M}$ is generated by a single finite group then $I\mathfrak{M}$ is generated by a single finite quasigroup?