Adapted splittings for pairs (G,W)

• Autor(a) principal: Andrade, Maria Gorete Carreira [UNESP]
• Data de Publicação: 2019
• Outros Autores: de Lourdes Campello Fanti, Ermínia [UNESP]
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1016/j.topol.2018.11.026; http://hdl.handle.net/11449/189949
• topic: Cohomology of groups; Duality; Ends of groups; Splitting of groups

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.