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A note about splittings of groups and commensurability under a cohomological point of view

Maria Gorete Carreira Andrade, Ermınia de Lourdes Campelloi Fanti

Abstract


Let G be a group, let S be a subgroup with infinite index in G and let FSG be a certain Z2G-module. In this paper, using the cohomological invariant E(G,S,FSG) or simply ˜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 ``singG(S)" defined by Kropholler and Roller ([8]. We conclude that ˜E(G,S) can substitute the  obstruction ``singG(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, commen-surability

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