Geodesic
Variations on a theme of Higman
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 9, Tome 289 (2002), pp. 57-62

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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. 
@article{ZNSL_2002_289_a2,
     author = {N. A. Vavilov and V. A. Petrov},
     title = {Variations on a theme of {Higman}},
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     publisher = {mathdoc},
     volume = {289},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_289_a2/}
}
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N. A. Vavilov; V. A. Petrov. Variations on a theme of Higman. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 9, Tome 289 (2002), pp. 57-62. http://geodesic.mathdoc.fr/item/ZNSL_2002_289_a2/