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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)



On the Gorenstein and cohomological dimension of groups

Author: Olympia Talelli
Journal: Proc. Amer. Math. Soc. 142 (2014), 1175-1180
MSC (2010): Primary 20J05; Secondary 55R35
Published electronically: January 30, 2014
MathSciNet review: 3162240
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Abstract: Here we relate the Gorenstein dimension of a group $ G$, $ \mathrm {Gcd}_{R}G$, over $ \mathbb{Z}$ and $ \mathbb{Q}$ to the cohomological dimension of $ G$, $ \mathrm {cd}_{R}G$, over $ \mathbb{Z}$ and $ \mathbb{Q}$, and show that if $ G$ is in $ {\scriptstyle \bf {LH}}\mathfrak{F}$, a large class of groups defined by Kropholler, then $ \mathrm {cd}_{\mathbb{Q}}G=\mathrm {Gcd}_{\mathbb{Q}}G$ and if $ G$ is torsion free, then $ \mathrm {Gcd}_{\mathbb{Z}}G= \mathrm {cd}_{\mathbb{Z}}G$. We also show that for any group $ G$, $ \mathrm {Gcd}_{\mathbb{Q}}G\leq \mathrm {Gcd}_{\mathbb{Z}}G$.

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Olympia Talelli
Affiliation: Department of Mathematics, University of Athens, Panepistimiopolis, GR-157 84, Athens, Greece

Received by editor(s): May 25, 2011
Received by editor(s) in revised form: April 25, 2012, and May 21, 2012
Published electronically: January 30, 2014
Additional Notes: This research supported by a GSRT/Greece excellence grant, cofounded by the ESF/EV and Natural Resources.
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.