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15.36 (2002)

Open

For a class $\mathcal{M}$ of groups let $L(\mathcal{M})$ be the class of groups $G$ such that the normal subgroup $\langle a^G \rangle$ generated by an element $a$ belongs to $\mathcal{M}$ for any $a \in G$. Is it true that the class $L(\mathcal{M})$ is finitely axiomatizable if $\mathcal{M}$ is the quasivariety generated by a finite group?

Contributor: A. I. Budkin

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