Remarks on the group algebra as symmetric algebra. II.

DOI10.1016/0021-8693(82)90063-1zbMath0488.16010OpenAlexW1990626325MaRDI QIDQ1165928

Burkhard Külshammer

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1016/0021-8693(82)90063-1

zbMATH Keywords

conjugacy classesdefect groupspower mapssymmetric algebrasblock ideals\(p\)-regular sectionsindex of nilpotency of Jacobson radicalmodular group algebras of finite groups

Mathematics Subject Classification ID

Group rings (16S34) Modular representations and characters (20C20) Quasi-Frobenius rings (16L60) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Radicals and radical properties of associative rings (16Nxx)

Related Items

Külshammer ideals of algebras of quaternion type, Derived equivalence classification of symmetric algebras of domestic type, The modular isomorphism problem: a survey, Loewy lengths of centers of blocks and exponents of defect groups, Abelian invariants and a reduction theorem for the modular isomorphism problem, On a theorem of Knörr, On group invariants determined by modular group algebras: even versus odd characteristic, The modular group algebra problem for metacyclic 𝑝-groups, DERIVED EQUIVALENCE CLASSIFICATION OF SYMMETRIC ALGEBRAS OF POLYNOMIAL GROWTH, A note on blocks with Abelian defect groups., On Loewy lengths of blocks, Finite-dimensional algebras arising as blocks of finite group algebras, On centers of blocks with one simple module, Blocks with transitive fusion systems, Lower bounds on Loewy lengths of centers of blocks, The modular isomorphism problem for two generated groups of class two, Quotients, Cartan matrices and Morita equivalent blocks, Remarks on the group algebra as symmetric algebra. III., On 2-blocks with \(k(B)-l(B)=1\).

Cites Work

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• On Brauer's theorem on sections in the theory of blocks of group characters
• Local properties of p-block algebras of finite groups
• Some studies on group algebras
• Remarks on the group algebra as symmetric algebra.
• Green correspondence between blocks with cyclic defect groups. I
• On the annihilator ideals of the radical of a group algebra
• The Radical of the Center of a Group Algebra
• Rank Element of a Projective Module
• On the Block of Defect Zero