We prove that torsion free subgroups of PGL2(C) (abstractly) commensurable with the Euclidean Bianchi groups are conjugacy separable. As a consequence we deduce the result stated in the title.

In a recent paper (cond-mat/0009279), Fabricius and McCoy studied the spectrum of the spin 1/2 XXZ model at roots of unity, i.e. ∆ = (q + q−1)/2 with q2N = 1 for integer N ≥ 2. They found a certain pattern of degeneracies and linked it to the sl2-loop symmetry present in the commensurable spin sector Sz ≡ 0 mod N . We show that the degeneracies are due to an unusual type of zero-energy “transpa...

We show that two uniform lattices of a regular right-angled Fuchsian building are commensurable, provided the chamber is a polygon with at least six edges. We show that in an arbitrary Gromov-hyperbolic regular right-angled building associated to a graph product of finite groups, a uniform lattice is commensurable with the graph product provided all of its quasiconvex subgroups are separable. W...

We prove that there are infinitely many pairwise non-commensurable hyperbolic $n$-manifolds have the same ambient group and trace ring, for any $n \geq 3$. The manifolds can be chosen compact if 4$.

Let G be a connected non-compact Q-simple real algebraic group defined over Q, that is, the identity component of the group of the real points of a connected Q-simple algebraic group which is R-isotropic. Let Γ ⊂ G(Q) be an arithmetic subgroup of G. As is well known, Γ has finite co-volume in G [BH]. Denote by μG the G-invariant Borel probability measure on Γ\G. Two subgroups Γ1 and Γ2 of G are...