Andrade, Maria Gorete Carreira [UNESP]Gazon, Amanda Buosi [UNESP]2015-04-272015-04-272014International Journal of Applied Mathematics, v. 27, n. 1, p. 13-20, 2014.1311-1728http://hdl.handle.net/11449/122696Based on the cohomology theory of groups, Andrade and Fanti defined in [1] an algebraic invariant, denoted by E(G,S, M), where G is a group, S is a family of subgroups of G with infinite index and M is a Z2G-module. In this work, by using the homology theory of groups instead of cohomology theory, we define an invariant ``dual'' to E(G, S, M), which we denote by E*(G, S, M). The purpose of this paper is, through the invariant E*(G, S, M), to obtain some results and applications in the theory of duality groups and group pairs, similar to those shown in Andrade and Fanti [2], and thus, providing an alternative way to get applications and properties of this theory.13-20enghomology of groupsdualitycohomological invariantsArtigo10.12732/ijam.v27i1.2Acesso aberto3186337502957366