Modular Representation Theory of Finite Groups with T. I. Sylow p-Subgroups

DOI10.2307/2001249zbMath0701.20007OpenAlexW4230705372MaRDI QIDQ3478595

Harvey I. Blau, Gerhard O. Michler

Publication date: 1990

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2001249

zbMATH Keywords

\(p\)-blocksAlperin-McKay conjecturedefect groupnumbers of irreducible complex charactersBrauer correspondentBrauer conjecturesnumbers of irreducible modular charactersheight zeroT.I. Sylow subgroups

Mathematics Subject Classification ID

Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Modular representations and characters (20C20)

Related Items (20)

The Alperin Weight Conjecture and Dade's Conjecture for the Simple Group J₄ ⋮ Controlled 2-blocks of quasisimple groups ⋮ On centres of 3-blocks of the Ree groups \(^2G_2(q)\) ⋮ \textit{ZJ}-controlled blocks of quasisimple groups for odd primes ⋮ A note on blocks of finite groups with TI Sylow \(p\)-subgroups ⋮ Minimal modular character degrees for groups with a cyclic Sylow subgroup ⋮ Dade's inductive conjecture for the Ree groups of type \(G_2\) in the defining characteristic ⋮ Uno's invariant conjecture for Steinberg's triality groups in defining characteristic. ⋮ Dade's invariant conjecture for Steinberg's triality groups \(^3D_4(2^n)\) in defining characteristic. ⋮ Perfect generalized characters inducing the Alperin-McKay conjecture. ⋮ Broué's Abelian defect group conjecture holds for the Janko simple group \(J_4\). ⋮ Dade's Invariant Conjecture for the Symplectic Group Sp₄(2ⁿ) and the Special Unitary Group SU₄(2²ⁿ) in Defining Characteristic ⋮ Controlled blocks of the finite quasisimple groups for odd primes. ⋮ On finite groups of \(p\)-local rank one and conjectures of Dade and Robinson ⋮ Modular representation theory of blocks with trivial intersection defect groups. ⋮ On TI and TI defect blocks ⋮ Nilpotent blocks of quasisimple groups for odd primes ⋮ Equivariant \(K\)-theory and Alperin's conjecture ⋮ Some problems in computational representation theory ⋮ Character Table of a Borel Subgroup of the Ree Groups ²F₄(q²)

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