Solution to the presentation problem for powers of the augmentation ideal of torsion free and torsion Abelian groups.

DOI10.1016/j.aim.2003.11.002zbMath1068.16032OpenAlexW2004333072MaRDI QIDQ1887445

Anthony Bak, Guoping Tang

Publication date: 26 November 2004

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2003.11.002

zbMATH Keywords

presentationstorsion-free Abelian groupshomologyaugmentation idealsintegral group ringsAbelian torsion groups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Derived series, central series, and generalizations for groups (20F14)

Related Items

The Augmentation Quotients of the Groups of Order 2⁵, II ⋮ On the structure of the augmentation quotient group for some nonabelian 2-groups ⋮ Bak's work on theK-theory of rings ⋮ Augmentation quotients for burnside rings of generalized dihedral groups ⋮ Augmentation quotients for Burnside rings of some finite \({p}\)-groups ⋮ A Bloch-Wigner complex for SL₂ ⋮ Structure of augmentation quotients of finite homocyclic Abelian groups. ⋮ A basis for augmentation quotients of finite Abelian groups. ⋮ The Stable Behavior of the Augmentation Quotients of the Groups of Order p⁵, I ⋮ Stability in graded rings associated with commutative augmented rings ⋮ The Augmentation Quotients of the Groups of Order 2⁵, I ⋮ On the Structure of Augmentation Quotient Groups for the Generalized Quaternion Group

Cites Work

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• Stable augmentation quotients of Abelian groups
• The periodicity in the graded ring associated with an integral group ring
• Group rings and their augmentation ideals
• Presenting powers of augmentation ideals and Pfister forms
• The associated graded ring of an integral group ring
• The Associated Graded Ring of a Group Ring
• On a Problem of Karpilovsky
• Presenting powers of augmentation ideals of elementary \(p\)-groups

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