Broué's Abelian defect group conjecture for the sporadic simple Janko group \(J_4\) revisited.

DOI10.1016/j.jalgebra.2013.02.005zbMath1298.20017arXiv1212.2775OpenAlexW2055140114WikidataQ122957361 ScholiaQ122957361MaRDI QIDQ401745

Shigeo Koshitani, Felix Noeske, Jürgen Müller

Publication date: 27 August 2014

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

Full work available at URL: https://arxiv.org/abs/1212.2775

zbMATH Keywords

sporadic simple groupsBroué conjectureAbelian defect groupssplendid derived equivalencesJanko group \(J_4\)

Mathematics Subject Classification ID

Simple groups: sporadic groups (20D08) Modular representations and characters (20C20) Representations of sporadic groups (20C34)

Related Items (1)

Broué's abelian defect group conjecture and 3-decomposition numbers of the sporadic simple Conway group \(Co_1\).

Uses Software

• GAP
• MeatAxe
• GAP Character Table Library
• SmallGroups Library
• CTblLib
• AtlasRep
• ATLAS Group Representations

Cites Work

• Broué's Abelian defect group conjecture holds for the double cover of the Higman-Sims sporadic simple group.
• Broué's Abelian defect group conjecture holds for the sporadic simple Conway group \(Co_3\).
• The Broué conjecture for the faithful 3-blocks of 4.\(M_{22}\).
• Broué's Abelian defect group conjecture holds for the Harada-Norton sporadic simple group \(HN\).
• Decomposition numbers of non-principal blocks of \(J_4\) for characteristic 3.
• Pointed groups and construction of modules
• On the vertices of irreducible modules
• Peakword condensation and submodule lattices: An application of the Meat- Axe
• Derived equivalences for group rings
• Broué's conjecture holds for principal 3-blocks with elementary Abelian defect group of order 9
• Broué's conjecture for non-principal 3-blocks of finite groups
• Broué's Abelian defect group conjecture for the Held group and the sporadic Suzuki group.
• Standard generators for sporadic simple groups
• Stable equivalences of Morita type for self-injective algebras and \(p\)-groups
• Broué's Abelian defect group conjecture holds for the Janko simple group \(J_4\).
• Crossed products and blocks with normal defect groups
• On Scott Modules and p-Permutation Modules: An Approach through the Brauer Morphism
• The Maximal Subgroups of J ₄
• The Subgroups of M₂₄, or How to Compute the Table of Marks of a Finite Group
• Computing Homomorphism Spaces between Modules over Finite Dimensional Algebras
• Splendid Equivalences: Derived Categories and Permutation Modules
• Computing Decompositions of Modules over Finite-Dimensional Algebras
• Determination of socle series using the condensation method
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