Publicação: Adapted splittings for pairs (G,W)
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Let G be a group, W a G-set with [G:Gw]=∞ for all w∈W, where Gw denotes the point stabilizer of w∈W. Considering the restriction map resW G:H1(G,Z2G)→∏w∈EH1(Gw,Z2G), where E is a set of orbit representatives for the G-action in W, we define an algebraic invariant denoted by E‾(G,W). In this paper, by using the relation of this invariant with the end e(G) defined by Freudenthal–Hopf–Specker and a Swarup's Theorem about splittings of groups adapted to a family of subgroups, we show, for G finitely generated and W a G-set which falls into many finitely G-orbits, that (G,W) is adapted if, and only if, E‾(G,W)≥2.
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Cohomology of groups, Duality, Ends of groups, Splitting of groups
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Inglês
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Topology and its Applications, v. 253, p. 17-24.
