Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6426164 | Advances in Mathematics | 2011 | 13 Pages |
Abstract
We show that the class of pairs (Î,H) of a group and a finite index subgroup which verify a conjecture of Moore about projectivity of modules over ZÎ satisfy certain closure properties. We use this, together with a result of Benson and Goodearl, in order to prove that Moore's conjecture is valid for groups which belongs to Kropholler's hierarchy LHF. For finite groups, Moore's conjecture is a consequence of a theorem of Serre, about the vanishing of a certain product in the cohomology ring (the Bockstein elements). Using our result, we construct examples of pairs (Î,H) which satisfy the conjecture without satisfying the analog of Serre's theorem.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Eli Aljadeff, Ehud Meir,