Geodesic
A note about splittings of groups and commensurability under a~cohomological point of view
Algebra and discrete mathematics, Tome 9 (2010) no. 2, pp. 1-10.

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Let $G$ be a group, let $S$ be a subgroup with infinite index in $G$ and let $\mathcal{F}_SG$ be a certain $\mathbb Z_2G$-module. In this paper, using the cohomological invariant $E(G,S,\mathcal{F}_SG)$ or simply $\tilde{E}(G,S)$ (defined in [2]), we analyze some results about splittings of group $G$ over a commensurable with $S$ subgroup which are related with the algebraic obstruction "$\mathrm{sing}_G(S)$" defined by Kropholler and Roller [8]. We conclude that $\tilde{E}(G,S)$ can substitute the obstruction "$\mathrm{sing}_G(S)$" in more general way. We also analyze splittings of groups in the case, when $G$ and $S$ satisfy certain duality conditions.
Keywords: Splittings of groups, cohomology of groups, commensurability. 
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     author = {Maria Gorete Carreira Andrade and Erm{\'\i}nia de Lourdes Campello Fanti},
     title = {A note about splittings of groups and commensurability under a~cohomological point of view},
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Maria Gorete Carreira Andrade; Ermínia de Lourdes Campello Fanti. A note about splittings of groups and commensurability under a~cohomological point of view. Algebra and discrete mathematics, Tome 9 (2010) no. 2, pp. 1-10. http://geodesic.mathdoc.fr/item/ADM_2010_9_2_a0/