This question is a follow up question to [this](https://mathoverflow.net/questions/57235/automorphisms-of-sl-n-mathbbz/57236#57236) 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](http://www.reference-global.com/doi/abs/10.1515/crll.1966.223.56) 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.



When is Out$(SL_n(R))$ a torsion group ?
This question has been studied even for non-commutative associative rings. See, for example Golubchik, I. Z.; Mikhalëv, A. V. Isomorphisms of the general linear group over an associative ring. Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1983, no. 3, 61–72. They prove that if the ring $R$ contains $1/2$ (that is $2$ is invertible), then every isomorphism $\phi: GL\_n(R)\to GL\_n(R)$, $n\ge 3$, is standard on the subgroup $GE\_n(R)$ generated by the elementary and diagonal matrices. "Standard" means "generated by an automorphism of $R$. 


