A note about splittings of groups and commensurability under a cohomological point of view

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Author(s):	Andrade, M. G. C. ; Fanti, E. L. C. Total Authors: 2
Document type:	Journal article
Source:	ALGEBRA & DISCRETE MATHEMATICS; v. 9, n. 2, p. 10-pg., 2010-01-01.
Abstract
Let G be a group, let S a subgroup with infinite index in G and let F(s)G be a certain Z(2)G-module. In this paper, using the cohomological invariant E(G, S, F(s)G) or simply E(G, S) (defined in [2]), we analyze some results about splittings of group C over a commensurable with S subgroup which are related with the algebraic obstruction "sing(G)(S)" defined by Kropholler and Roller ([8]. We conclude that E(G,S) can substitute the obstruction "sing(G)(S)" in more general way. We also analyze splittings of groups in the case, when G and S satisfy certain duality conditions. (AU)