Sone remarks on eigeyvalues of the cartan matrix in finite groups

DOI10.1080/00927879308824769zbMath0815.20011OpenAlexW2061379087MaRDI QIDQ3141923

Masao Kiyota, Tomoyuki Wada

Publication date: 6 September 1994

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

Full work available at URL: https://doi.org/10.1080/00927879308824769

zbMATH Keywords

finite groupsCartan matrixeigenvaluesgroup algebra\(p\)-solvable groupsblocksindex of nilpotencydefect groupirreducible Brauer character\(p\)-blocknormal \(p\)-subgroupFrobenius rootsradical of block ideal

Mathematics Subject Classification ID

Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Modular representations and characters (20C20) Group rings of finite groups and their modules (group-theoretic aspects) (20C05)

Related Items (11)

Rationality of eigenvalues of Cartan matrices in finite groups ⋮ Eigenvector matrices of Cartan matrices for finite groups. ⋮ A counterexample to a conjecture of Wada ⋮ Eigenvalues of Cartan matrices of principal 3-blocks of finite groups with Abelian Sylow 3-subgroups. ⋮ The heights of irreducible Brauer characters in 2-blocks of the symmetric groups. ⋮ On Willems' conjecture on Brauer character degrees ⋮ Eigenvalues of Cartan matrices of principal 2-blocks with Abelian defect groups. ⋮ On degrees of irreducible Brauer characters ⋮ Eigenvalues and elementary divisors of Cartan matrices of cyclic blocks with \(l(B)\leqslant 5\) and tame blocks. ⋮ ON THE FROBENIUS–PERRON EIGENVALUES OF CARTAN MATRICES FOR SOME FINITE GROUPS ⋮ A local conjecture on Brauer character degrees of finite groups

Cites Work

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• The loewy structure of the projective indecomposable modules for a₈in characteristic 2
• The loewy structure of the projective indecomposable modules for a₉in characteristic 2
• Projective Modules, Filtrations and Cartan Invariants
• Algebras and Dihedral Defect Groups
• Algebras and Semidihedral Defect Groups I
• On the radical of a group algebra

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