The multiplicative Jordan decomposition in group rings. II.

DOI10.1016/j.jalgebra.2007.07.009zbMath1144.16020OpenAlexW2036213268MaRDI QIDQ2460805

Lawrence E. Wilson, Alfred W. Hales, Inder Bir Singh Passi

Publication date: 16 November 2007

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2007.07.009

zbMATH Keywords

dihedral groupsgeneralized quaternion groupsintegral group ringsfinite 2-groupsunipotent elementsWedderburn decompositionssemisimple elementsadditive Jordan decompositionsmultiplicative Jordan decompositions

Mathematics Subject Classification ID

Group rings (16S34) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Finite nilpotent groups, (p)-groups (20D15) Units, groups of units (associative rings and algebras) (16U60)

Related Items (10)

Group algebras. ⋮ Nilpotent decomposition in integral group rings ⋮ Group rings and Jordan decomposition ⋮ Products of unipotent elements in certain algebras ⋮ Multiplicative Jordan decomposition in group rings and \(p\)-groups with all noncyclic subgroups normal. ⋮ Corrigendum to ``The multiplicative Jordan decomposition in group rings. II. ⋮ Multiplicative Jordan Decomposition in Group Rings of 3-Groups, II ⋮ MULTIPLICATIVE JORDAN DECOMPOSITION IN GROUP RINGS OF 2, 3-GROUPS ⋮ MULTIPLICATIVE JORDAN DECOMPOSITION IN GROUP RINGS OF 3-GROUPS ⋮ The multiplicative Jordan decomposition in the integral group ring \(\mathbb{Z} [Q_8 \times C_p\)]

Cites Work

• Integral group rings with Jordan decomposition
• The decomposition of a linear mapping
• The multiplicative Jordan decomposition in group rings
• Das ``schiefe Produkt in der Gruppentheorie mit Anwendung auf die endlichen nichtkommutativen Gruppen mit lauter kommutativen echten Untergruppen und die Ordnungszahlen, zu denen nur kommutative Gruppen gehören
• Partial augmentations and jordan decomposition in group ring
• Degree problems of representation theory over arbitrary fields of characteristic 0. On theorems of N. Ito and J. G: Thompson.
• Jordan decomposition and hypercentral units in integral group rings
• MULTIPLICATIVE JORDAN DECOMPOSITION IN INTEGRAL GROUP RINGS OF GROUPS OF ORDER 16
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