Bianchi groups are conjugacy separable. (Q964526)

A group \(G\) is conjugacy separable if whenever \(x\) and \(y\) are non-conjugate elements of \(G\), there exists some finite quotient of \(G\) in which the images of \(x\) and \(y\) are non-conjugate. The Bianchi groups are defined as \(\text{PSL}_2(O_d)\), where \(O_d\) denotes the ring of integers of the field \(\mathbb{Q}(\sqrt{-d})\) for each square-free positive integer \(d\). The authors prove that non-uniform arithmetic lattices of \(\text{SL}_2(\mathbb{C})\) and consequently the Bianchi groups are conjugacy separable. The proof is based on recent deep resuls of \textit{I. Agol, D. D. Long, A. W. Reid} [Ann. Math. (2) 153, No. 3, 599-621 (2001; Zbl 1067.20067)] and Minasyan. The same methods also allow the authors to prove conjugacy separability of virtually limit groups.