This question is a follow up question to ![this][1] question. So my question is: For which rings $R$ (commutative, with unit) (and which integers $n$) is $Out(SL_n(R))$ a torsion group? A consequence of Theorem A and B in ![O'Meara The automorphisms of the linear groups over any integral domain][2] is that this is the case (for $n\ge 3$) for any integral domain, whose underlying additive abelian group is finitely generated. However this is just a computation and I am wondering, whether this question has already been studied somewhere more systematically or if there are other results that also have such a corollary. [1]: http://mathoverflow.net/questions/57235/automorphisms-of-sl-n-mathbbz/57236#57236 [2]: http://www.reference-global.com/doi/abs/10.1515/crll.1966.223.56