Abstract:
Let $L_q(qG)$ be the quasivariety lattice contained in a quasivariety generated by a group $G$. It is proved that if $G$ is a finitely generated torsion-free group in $\mathcal A\mathcal B_{2^n}$ (i.e., $G$ is an extension of an Abelian group by a group of exponent $2^n$), which is a split extension of an Abelian group by a cyclic group, then the lattice $L_q(qG)$ is a finite chain.
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