Abstract
We show that the class of pairs (Γ, H ) of a group and a finite index subgroup which verify a conjecture of Moore about projectivity of modules over ZΓ 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 (Γ, H ) which satisfy the conjecture without satisfying the analog of Serre’s theorem.
Original language | English |
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Pages (from-to) | 4212-4224 |
Journal | Advances in Mathematics |
Volume | 226 |
DOIs | |
Publication status | Published - 20 Mar 2011 |
Externally published | Yes |