Maria Gorete Carreira Andrade1, Amanda Buosi Gazon2
1,2 Department of Mathematics - IBILCE
UNESP - São Paulo State University
Rua Cristovão Colombo, 2265
15054 - 000 - São José do Rio Preto - SP, BRAZIL
Abstract. Based on the cohomology theory of groups, Andrade and Fanti defined in  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 , and thus, providing an alternative way to get applications and properties of this theory.
AMS Subject classification: 20E06, 05C25, 20J06
Keywords and phrases: homology of groups, duality, cohomological invariants
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