Nilpotency of Bocksteins, Kropholler's hierarchy and a conjecture of Moore |
| |
Authors: | Eli Aljadeff Ehud Meir |
| |
Institution: | Technion-Israel Institute of Technology, Haifa, Israel |
| |
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. |
| |
Keywords: | Cohomology of groups Kropholler's hierarchy LHF Moore's conjecture Projectivity over group rings |
本文献已被 ScienceDirect 等数据库收录! |
|