Homological finiteness conditions for pro-pgroups

DOI10.1080/00927879908826743zbMath0939.20026OpenAlexW2033334988MaRDI QIDQ4265562

J. D. King

Publication date: 10 April 2000

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927879908826743

zbMATH Keywords

projective resolutionshomology groupsfinitely generated pro-\(p\) groupsfinitely presented pro-\(p\) groupsmetabelian pro-\(p\) groups

Mathematics Subject Classification ID

Solvable groups, supersolvable groups (20F16) Generators, relations, and presentations of groups (20F05) Homological methods in group theory (20J05) Limits, profinite groups (20E18)

Related Items (21)

On profinite groups of type \(\mathrm{FP}_\infty\). ⋮ The torsion-free rank of homology in towers of soluble pro-\(p\) groups ⋮ Bieri-Eckmann criteria for profinite groups ⋮ On the Growth of Noetherian Filtered Rings ⋮ Coabelian ideals in \(\mathbb{N}\)-graded Lie algebras and applications to right angled Artin Lie algebras ⋮ Finiteness conditions on subgroups of profinite \(p\)-Poincaré duality groups. ⋮ Weak commutativity for pro-\(p\) groups ⋮ Right‐angled Artin pro‐p$p$ groups ⋮ On pro-\(p\) analogues of limit groups via extensions of centralizers. ⋮ Subdirect products of pro-p groups ⋮ Centre-by-metabelian pro-p groups of type FP_m ⋮ Pro-\(\mathcal {C}\) completions of orientable \(\mathrm{PD}^3\)-pairs ⋮ On subdirect products of free pro-\(p\) groups and Demushkin groups of infinite depth. ⋮ Pro-\(p\) completions of Poincaré duality groups. ⋮ Homological finiteness properties of pro-\(p\) modules over metabelian pro-\(p\) groups. ⋮ Growth of Homology of Centre-by-metabelian Pro- Groups ⋮ Bass-Serre theory for Lie algebras: a homological approach ⋮ Embedding properties of metabelian pro-p groups ⋮ Uncountably many non-commensurable pro-p groups of homological type FPk but not FPk+1 ⋮ SUBDIRECT PRODUCTS OF FREE PRO-p AND DEMUSHKIN GROUPS ⋮ On a conjecture of E. Rapaport Strasser about knot-like groups and its pro-\(p\) version.

Cites Work

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• EMBEDDING THEOREMS FOR PROFINITE GROUPS
• Valuations and Finitely Presented Metabelian Groups
• Noetherian Rings of Finite Global Dimension
• Metabelian Groups of Type (FP )_∞ are Virtually of Type (FP )
• Some Remarks on Tensor, Symmetric and Exterior Powers of Modules over an Abelian Group
• Embedding theorems for pro-p groups
• Polynomial Identities in Graded Group Rings, Restricted Lie Algebras and p-Adic Analytic Groups
• On the Dimension of Group Rings

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