Jordan conjecture for fundamental groups of log canonical Fano pairs

Let $n$ be a positive integer, and let $(X,\Delta)$ be a log canonical Fano pair. Write $\pi_1^{\rm orb}(X,\Delta)$ for its orbifold fundamental group. Jordan conjecture for log canonical Fano pairs. There exists a constant $c(n)$ such that there is a short exact sequence

$$1\rightarrow A \rightarrow \pi_1^{\rm orb}(X,\Delta)\rightarrow N \rightarrow 1,$$

where $A$ is an abelian group of rank at most $n$ and $N$ is a finite group of order at most $c(n)$. The conjecture predicts a uniform Jordan-type bound for orbifold fundamental groups of higher-dimensional log canonical Fano pairs; the paper presents it as an expectation beyond the cases established by its results.