Andrade, Maria Gorete Carreira [UNESP]Fanti, Ermínia de Lourdes Campello [UNESP]2015-04-272015-04-272012International Journal of Applied Mathematics, v. 25, n. 2, p. 183-190, 2012.1311-1728http://hdl.handle.net/11449/122693Let G be a group, W a nonempty G-set and M a Z2G-module. Consider the restriction map resG W : H1(G,M) → Pi wi∈E H1(Gwi,M), [f] → (resGG wi [f])i∈I , where E = {wi, i ∈ I} is a set of orbit representatives in W and Gwi = {g ∈ G | gwi = wi} is the G-stabilizer subgroup (or isotropy subgroup) of wi, for each wi ∈ E. In this work we analyze some results presented in Andrade et al [5] about splittings and duality of groups, using the point of view of Dicks and Dunwoody [10] and the invariant E'(G,W) := 1+dimkerresG W, defined when Gwi is a subgroup of infinite index in G for all wi in E, andM = Z2 (where dim = dimZ2). We observe that the theory of splittings of groups (amalgamated free product and HNN-groups) is inserted in the combinatory theory of groups which has many applications in graph theory (see, for example, Serre [12] and Dicks and Dunwoody [10]).183-190engcohomology of groupsdualitysplittings of groupsArtigoAcesso aberto31863375029573660358661907070998