Variations on a theme of Higman

Let R be an associative ring with 1, $n\ge3$ We show that Higman's computation of the first cohomology group of the special linear group over a field with natural coefficients really shows that $H^1(\operatorname{St}(n,R),R^n)=0$ for $n\ge4$ and explicitly compute this group for $n=3$, when it does not vanish. In [6] the second-named author extended these results to all classical Steinberg groups.