Finite group algebras of nilpotent groups: a complete set of orthogonal primitive idempotents.

DOI10.1016/j.ffa.2010.10.005zbMath1215.20006arXiv1302.3882OpenAlexW3100961985MaRDI QIDQ630809

Gabriela Olteanu, Inneke Van Gelder

Publication date: 21 March 2011

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.3882

zbMATH Keywords

finite fieldsrepresentation theorygroup ringscoding theoryWedderburn decompositionsprimitive central idempotentssemisimple group algebras

Mathematics Subject Classification ID

Group rings (16S34) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Finite nilpotent groups, (p)-groups (20D15)

Related Items (6)

On matrix units of semisimple group algebras ⋮ Primitive idempotent tables of cyclic and constacyclic codes ⋮ Group rings of finite strongly monomial groups: central units and primitive idempotents. ⋮ Primitive idempotents of Schur rings. ⋮ Finite semisimple group algebra of a normally monomial group ⋮ Construction of minimal non-abelian left group codes

Uses Software

• GAP
• wedderga

Cites Work

• Wedderburn decomposition of finite group algebras.
• Idempotents in group algebras and minimal abelian codes
• Metacyclic error-correcting codes
• On Monomial Characters and Central Idempotents of Rational Group Algebras
• The Group of Automorphisms of the Rational Group Algebra of a Finite Metacyclic Group
• CENTRAL IDEMPOTENTS IN THE RATIONAL GROUP ALGEBRA OF A FINITE NILPOTENT GROUP
• The schur subgroup of the brauer group
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