Geodesic
On the homological dimension of group algebras of solvable groups
Izvestiya. Mathematics , Tome 5 (1971) no. 6, pp. 1231-1244.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper we calculate the weak dimension of the group algebra of a solvable group and the projective dimension of the group algebra of a countable nilpotent group. Exact bounds are obtained for the projective dimension of the group algebra of a torsion-free solvable group. For the case that the principal ring is commutative and Noetherian we obtain corresponding results for global dimensions. On the assumption that the principal ring is a field we prove the additivity of projective and weak dimension on a class of groups for which there exists a finitely generated projective resolvent of the principal ring. 
@article{IM2_1971_5_6_a3,
     author = {G. L. Fel'dman},
     title = {On the homological dimension of group algebras of solvable groups},
     journal = {Izvestiya. Mathematics },
     pages = {1231--1244},
     publisher = {mathdoc},
     volume = {5},
     number = {6},
     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1971_5_6_a3/}
}
TY  - JOUR
AU  - G. L. Fel'dman
TI  - On the homological dimension of group algebras of solvable groups
JO  - Izvestiya. Mathematics 
PY  - 1971
SP  - 1231
EP  - 1244
VL  - 5
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1971_5_6_a3/
LA  - en
ID  - IM2_1971_5_6_a3
ER  - 
%0 Journal Article
%A G. L. Fel'dman
%T On the homological dimension of group algebras of solvable groups
%J Izvestiya. Mathematics 
%D 1971
%P 1231-1244
%V 5
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1971_5_6_a3/
%G en
%F IM2_1971_5_6_a3
G. L. Fel'dman. On the homological dimension of group algebras of solvable groups. Izvestiya. Mathematics , Tome 5 (1971) no. 6, pp. 1231-1244. http://geodesic.mathdoc.fr/item/IM2_1971_5_6_a3/

[1] Balcerzuk S., “The global dimension of the group rings of abelian groups. III”, Fundam. math., 67 (1970), 241–250 | MR

[2] Grotendik A., O nekotorykh voprosakh gomologicheskoi algebry, IL., M., 1961

[3] Gruenberg K., Cohomological topics in group theory, Lecture Notes in Math., 143, Springer, 1970 | MR | Zbl

[4] Kartan A., Eilenberg S., Gomologicheskaya algebra, IL, M., 1960

[5] Kurosh A. G., Teoriya grupp, Nauka, M., 1967 | MR | Zbl

[6] Maklein S., Gomologiya, Mir, M., 1966

[7] Maltsev A. I., “O nekotorykh klassakh beskonechnykh razreshimykh grupp”, Matem. sb., 28 (1951), 567–588

[8] Stammbach U., “On the weak homological dimension of the group algebra of soluble group”, J. London Math. Soc., 2 (1970), 567–570 | MR | Zbl

[9] Swan R., “Groups of cohomological dimension one”, J. Algebra, 12 (1969), 585–610 | DOI | MR | Zbl

[10] Wall C. T. C., “Resolutions for extensions of groups”, Proc. Cambridge Philos. Soc., 57 (1961), 251–255 | DOI | MR | Zbl

[11] Charin V. S., “O razreshimykh gruppakh tipa $A_4$”, Matem. sb., 52 (1960), 895–914 | Zbl