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

SN - 0001-8708

VL - 226

SP - 4212

EP - 4224

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 5

ER -