TY - JOUR
T1 - Nilpotency of Bocksteins, Kropholler's hierarchy and a conjecture of Moore
AU - Aljadeff, Eli
AU - Meir, Ehud
N1 - Funding Information:
The first author was supported by the Israel Science Foundation (grant No. 1283/08) and by the E. Schaver Research Fund.
PY - 2011/3/20
Y1 - 2011/3/20
N2 - 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.
AB - 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.
KW - Cohomology of groups
KW - Kropholler's hierarchy
KW - LHF
KW - Moore's conjecture
KW - Projectivity over group rings
UR - http://www.scopus.com/inward/record.url?scp=79551582460&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2010.12.002
DO - 10.1016/j.aim.2010.12.002
M3 - 文章
AN - SCOPUS:79551582460
VL - 226
SP - 4212
EP - 4224
JO - Advances in Mathematics
JF - Advances in Mathematics
SN - 0001-8708
IS - 5
ER -