A dual homological invariant and some properties

• Autor(a) principal: Andrade, Maria Gorete Carreira [UNESP]
• Data de Publicação: 2014
• Outros Autores: Gazon, Amanda Buosi [UNESP]
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://www.diogenes.bg/ijam/contents/2014-27-1/2/; http://hdl.handle.net/11449/122696
• topic: homology of groups; duality; cohomological invariants

Based 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.