The multiplicative Jordan decomposition in group rings

DOI10.1006/jabr.1998.7557zbMath0919.16021OpenAlexW4210529999MaRDI QIDQ1277012

Satya R. Arora, Inder Bir Singh Passi, Alfred W. Hales

Publication date: 8 September 1999

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

Full work available at URL: https://doi.org/10.1006/jabr.1998.7557

zbMATH Keywords

finite groupsdihedral groupsgeneralized quaternion groupsintegral group ringsmultiplicative decompositionsadditive 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)

Related Items (13)

MULTIPLICATIVE JORDAN DECOMPOSITION IN INTEGRAL GROUP RINGS OF GROUPS OF ORDER 16 ⋮ Group algebras. ⋮ 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. ⋮ Multiplicative Jordan decomposition in group rings with a Wedderburn component of degree 3. ⋮ 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 \(\mathbb{Z} [Q_8 \times C_p\)] ⋮ Jordan decompositions in alternative loop rings ⋮ Integral Jordan decomposition of matrices

Cites Work

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• Integral group rings with Jordan decomposition
• Units in \({\mathbb{Z}}[Q_ p\)]
• Nilpotent elements in group rings
• Central height of the unit group of an integral group ring
• Partial augmentations and jordan decomposition in group ring
• Jordan decomposition and hypercentral units in integral group rings

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