On the Gorenstein and cohomological dimension of groups

Here we relate the Gorenstein dimension of a group G, Gcd R G, over ℤ and ℚ to the cohomological dimension of G, cd R G, over ℤ and ℚ, and show that if G is in LHℱ, a large class of groups defined by Kropholler, then cd ℚ G = Gcd ℚ G and if G is torsion free, then Gcd ℤ G = cd ℤ G. We also show that...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2014-04, Vol.142 (4), p.1175-1180
Main Author: TALELLI, OLYMPIA
Format: Article
Language:English
Subjects:
Algebra
Commutativity
Integers
Jumping
Mathematical theorems
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Summary:Here we relate the Gorenstein dimension of a group G, Gcd R G, over ℤ and ℚ to the cohomological dimension of G, cd R G, over ℤ and ℚ, and show that if G is in LHℱ, a large class of groups defined by Kropholler, then cd ℚ G = Gcd ℚ G and if G is torsion free, then Gcd ℤ G = cd ℤ G. We also show that for any group G, Gcd ℚ G ≤ Gcd ℤ G.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-2014-11883-1