I am looking (for $n,k\in{\mathbb Z}$) for a presentation (in the best of all worlds concretely, as a list of relators) for the group ${\rm SL}_n(R)$ for $R={\mathbb Z}[\frac{1}{k}]=\{\frac{a}{k^l}\mid a\in {\mathbb Z}\}$.

A search in MathSciNet found a paper of Behr and Mennicke(A presentation of the groups PSL(2,p), Can. J. Math. 20, 1432-1438 (1968)) that gives a presentation for the special case of $n=k=2$; (add the diagonal matrix $(2,\frac{1}{2})$ as extra generator and describe its conjugation action on suitable generators of ${\rm SL}_n({\mathbb Z})$); but a reference search did not yield a further result.

Similarly mathOverflow carried the same question question for other rings, but not $R$.

(A follow-up question would be the same question for ${\rm Sp}$)