Homology of free Abelianized extensions of groups
Sbornik. Mathematics, Tome 72 (1992) no. 2, pp. 503-518 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $G$ be a group given by a free presentation $G=F/N$, and $N'$ the commutator subgroup of $N$. The quotient $F/N'$ is called a free abelianized extension of $G$. We study the homology of $F/N'$ with trivial coefficients. In particular, for torsion-free $G$ our main result yields a complete description of the odd torsion in the integral homology of $F/N'$ in terms of the mod $p$ homology of $G$.
@article{SM_1992_72_2_a13,
     author = {L. G. Kovacs and Yu. V. Kuz'min and R. Stohr},
     title = {Homology of free {Abelianized} extensions of groups},
     journal = {Sbornik. Mathematics},
     pages = {503--518},
     year = {1992},
     volume = {72},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1992_72_2_a13/}
}
TY  - JOUR
AU  - L. G. Kovacs
AU  - Yu. V. Kuz'min
AU  - R. Stohr
TI  - Homology of free Abelianized extensions of groups
JO  - Sbornik. Mathematics
PY  - 1992
SP  - 503
EP  - 518
VL  - 72
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1992_72_2_a13/
LA  - en
ID  - SM_1992_72_2_a13
ER  - 
%0 Journal Article
%A L. G. Kovacs
%A Yu. V. Kuz'min
%A R. Stohr
%T Homology of free Abelianized extensions of groups
%J Sbornik. Mathematics
%D 1992
%P 503-518
%V 72
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1992_72_2_a13/
%G en
%F SM_1992_72_2_a13
L. G. Kovacs; Yu. V. Kuz'min; R. Stohr. Homology of free Abelianized extensions of groups. Sbornik. Mathematics, Tome 72 (1992) no. 2, pp. 503-518. http://geodesic.mathdoc.fr/item/SM_1992_72_2_a13/

[1] Kuzmin Yu. V., “Gomologii grupp vida $F/N'$”, DAN SSSR, 296 (1987), 267–270 | MR

[2] Kuzmin Yu. V., “Homology theory of free abelianized extensions”, Communications in Algebra, 16:12 (1988), 2447–2533 | DOI | MR

[3] Kuzmin Yu. V., “O nekotorykh svoistvakh svobodnykh abelevykh rasshirenii”, Matem. sb., 180(222) (1989), 850–862 | MR

[4] Zerck R., “On the homology of free abelianized extensions of finite groups”, J. Pure Appl. Algebra, 1990 | MR

[5] Hartley B., Stöhr R., A note on the homology of free abelianized extensions, Preprint, 1990 | MR

[6] Kuzmin Yu. V., “Ob elementakh konechnogo poryadka v svobodnykh gruppakh nekotorykh mnogoobrazii”, Matem. sb., 119(161) (1982), 119–131 | MR

[7] Stöhr R., “On elements of order four in certain free central extensions of groups”, Math. Proc. Cambridge Philos. Soc., 106 (1989), 13–28 | DOI | MR | Zbl

[8] Hannebauer T., Stöhr R., “Homology of groups with coefficients in free metabelian Lie powers and exterior powers of relation modules and applications to group theory”, Rend. Circ. Mat. Palermo, Ser. 2, Proc. Second Internat. Group Theory Conf. (Bressanone/Brixen. 1989), no. 23, 77–113 | MR | Zbl

[9] Hartley B., Stöhr R., “Homology of higher relation modules and torsion in free central extensions of groups”, Proc. London Math. Soc., 3 (1991) | MR