Baer's conjecture on Noetherian group rings

Let $G$ be a group, and let $\a0\mathbb{Z}G$ be its group ring. The group ring is Noetherian if it satisfies the ascending chain condition on ideals.

Baer's conjecture. If $\mathbb{Z}G$ is Noetherian, then $G$ is polycyclic-by-finite.

The conjecture concerns the relationship between ring-theoretic finiteness of a group ring and structural finiteness of the underlying group. The paper confirms it for virtually RFRS groups of type $\mathrm{FP}(\mathbb{Q})$, while the general statement is presented as a longstanding conjecture.