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 
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/
@article{ZNSL_2002_289_a2,
     author = {N. A. Vavilov and V. A. Petrov},
     title = {Variations on a theme of {Higman}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {57--62},
     year = {2002},
     volume = {289},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_289_a2/}
}
TY  - JOUR
AU  - N. A. Vavilov
AU  - V. A. Petrov
TI  - Variations on a theme of Higman
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2002
SP  - 57
EP  - 62
VL  - 289
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2002_289_a2/
LA  - ru
ID  - ZNSL_2002_289_a2
ER  - 
%0 Journal Article
%A N. A. Vavilov
%A V. A. Petrov
%T Variations on a theme of Higman
%J Zapiski Nauchnykh Seminarov POMI
%D 2002
%P 57-62
%V 289
%U http://geodesic.mathdoc.fr/item/ZNSL_2002_289_a2/
%G ru
%F ZNSL_2002_289_a2

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.