Aritmethic lattices of $\SO(1,n)$ and units of group rings

Abstract

We establish that standard arithmetic subgroups of a special orthogonal group $\mathrm{SO}(1,n)$ are conjugacy separable. As an application we deduce this property for unit groups of certain integer group rings. We also prove that finite quotients of group of units of any of these group rings determines the original group ring.

Theorem 1.1 is stated in slightly more general form. We introduced Remarks 3.6 and 3.8 explaining why the proofs work for this more general statement and made appropriate changes (using reference [38] instead of [3] in the present version) in the proofs of Theorem 1.1 and 1.2. The results are unchanged