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|Type:||Artigo de periódico|
|Title:||A note on projective and flat dimensions and the Bieri-Neumann-Strebel-Renz Sigma-invariants|
|Abstract:||Let G he a finitely generated group, and A a Z [G]-module of flat dimension n such that the homological invariant Sigma(n)(G, A) is not empty. We show that A has projective dimension n as a Z[G]-module. In particular, if G is a group of homological dimension hd(G) = n such that the homological invariant Sigma(n)(G, Z) is not empty, then G has cohomological dimension cd(G) = n. We show that if G is a finitely generated soluble group, the converse is true subject to taking a subgroup of finite index, i.e., the equality cd(G) = hd(G) implies that there is a subgroup H of finite index in G such that Sigma(infinity)(H, Z) not equal 0.|
|Editor:||Taylor & Francis Inc|
|Appears in Collections:||Artigos e Materiais de Revistas Científicas - Unicamp|
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