Nilpotency of Bocksteins, Kropholler's hierarchy and a conjecture of Moore

Eli Aljadeff, Ehud Meir*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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 languageEnglish
Pages (from-to)4212-4224
Number of pages13
JournalAdvances in Mathematics
Issue number5
StatePublished - 20 Mar 2011
Externally publishedYes


  • Cohomology of groups
  • Kropholler's hierarchy
  • LHF
  • Moore's conjecture
  • Projectivity over group rings


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