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- Title
HOMOLOGICAL FINITENESS PROPERTIES OF WREATH PRODUCTS.
- Authors
BARTHOLDI, LAURENT; DE CORNULIER, YVES; KOCHLOUKOVA, DESSISLAVA H.
- Abstract
We study the homological finiteness properties FPm of wreath products Γ = H × G. We show that, when H has infinite abelianization, Γ is of type FPm if and only if both G and H have type FPm and G acts (diagonally) on Xi with stabilizers of type FPm-i and with finitely many orbits for all 1 ≤ i ≤ m. If furthermore H is torsion-free, we give a criterion for Γ to be Bredon-FPm with respect to the class of finite subgroups of Γ. Finally, when H has infinite abelianization and χ : Γ → R is a non-zero homomorphism with χ(H) = 0, we classify when [χ] belongs to the Bieri-Neumann-Strebel-Renz invariant Σm(Γ, Z).
- Subjects
HOMOLOGICAL algebra; WREATH products (Group theory); ABELIAN groups; MATHEMATICAL symmetry; HOMOMORPHISMS; HOMOTOPY theory
- Publication
Quarterly Journal of Mathematics, 2015, Vol 66, Issue 2, p437
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmath/hau035