Multiplicative Jordan decomposition in group rings and \(p\)-groups with all noncyclic subgroups normal.

DOI10.1016/j.jalgebra.2012.07.010zbMath1276.16021OpenAlexW2070653756MaRDI QIDQ1952140

Chia-Hsin Liu

Publication date: 27 May 2013

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2012.07.010

zbMATH Keywords

unitsfinite \(p\)-groupsintegral group ringsunipotent elementssemisimple 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 (4)

Nilpotent decomposition in integral group rings ⋮ Group rings and Jordan decomposition ⋮ Multiplicative Jordan decomposition in group rings with a Wedderburn component of degree 3. ⋮ Groups with Certain Normality Conditions

Cites Work

• The multiplicative Jordan decomposition in group rings
• The multiplicative Jordan decomposition in group rings. II.
• Nonnormal subgroups of \(p\)-groups.
• 2-groups with normal noncyclic subgroups
• A complete classification of finite p-groups all of whose noncyclic subgroups are normal
• MULTIPLICATIVE JORDAN DECOMPOSITION IN GROUP RINGS OF 2, 3-GROUPS
• MULTIPLICATIVE JORDAN DECOMPOSITION IN GROUP RINGS OF 3-GROUPS
• MULTIPLICATIVE JORDAN DECOMPOSITION IN INTEGRAL GROUP RINGS OF GROUPS OF ORDER 16

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