Geodesic
Some properties of $E(G,W,\mathcal{F}_TG)$ and~an~application in the theory of splittings of~groups
Algebra and discrete mathematics, Tome 30 (2020) no. 2, pp. 179-193

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

Let us consider $W$ a $G$-set and $M$ a $\mathbb{Z}_2G$-module, where $G$ is a group. In this paper we investigate some properties of the cohomological the theory of splittings of groups. Namely, we give a proof of the invariant $E(G,W,M)$, defined in [5] and present related results with independence of $E(G,W,M)$ with respect to the set of $G$-orbit representatives in $W$ and properties of the invariant $E(G,W,\mathcal{F}_TG)$ establishing a relation with the end of pairs of groups $\widetilde{e}(G,T)$, defined by Kropphller and Holler in [15]. The main results give necessary conditions for $G$ to split over a subgroup $T$, in the cases where $M=\mathbb{Z}_2(G/T)$ or $M=\mathcal{F}_TG$.
Keywords: cohomology of groups, cohomological invariants, splittings and derivation of groups. 
@article{ADM_2020_30_2_a2,
     author = {E. L. C. Fanti and L. S. Silva},
     title = {Some properties of $E(G,W,\mathcal{F}_TG)$ and~an~application in the theory of splittings of~groups},
     journal = {Algebra and discrete mathematics},
     pages = {179--193},
     publisher = {mathdoc},
     volume = {30},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2020_30_2_a2/}
}
TY  - JOUR
AU  - E. L. C. Fanti
AU  - L. S. Silva
TI  - Some properties of $E(G,W,\mathcal{F}_TG)$ and~an~application in the theory of splittings of~groups
JO  - Algebra and discrete mathematics
PY  - 2020
SP  - 179
EP  - 193
VL  - 30
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2020_30_2_a2/
LA  - en
ID  - ADM_2020_30_2_a2
ER  - 
%0 Journal Article
%A E. L. C. Fanti
%A L. S. Silva
%T Some properties of $E(G,W,\mathcal{F}_TG)$ and~an~application in the theory of splittings of~groups
%J Algebra and discrete mathematics
%D 2020
%P 179-193
%V 30
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2020_30_2_a2/
%G en
%F ADM_2020_30_2_a2
E. L. C. Fanti; L. S. Silva. Some properties of $E(G,W,\mathcal{F}_TG)$ and~an~application in the theory of splittings of~groups. Algebra and discrete mathematics, Tome 30 (2020) no. 2, pp. 179-193. http://geodesic.mathdoc.fr/item/ADM_2020_30_2_a2/