Proving a conjecture for fusion systems on a class of groups

DOI10.1016/j.jalgebra.2023.09.043zbMath1527.20025arXiv2302.05203OpenAlexW4387614386MaRDI QIDQ6066497

Patrick Serwene

Publication date: 16 November 2023

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

Full work available at URL: https://arxiv.org/abs/2302.05203

zbMATH Keywords

fusion systemsblocks, saturated fusion system, exotic fusion system

Mathematics Subject Classification ID

Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Modular representations and characters (20C20) Representations of finite groups of Lie type (20C33)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quasi-isolated blocks and Brauer's height zero conjecture.
• Derived categories and Deligne-Lusztig varieties. II.
• 3-blocks and 3-modular characters of \(G_ 2(q)\)
• Fusion systems over a Sylow \(p\)-subgroup of \(\mathrm{G}_2(p)\)
• The blocks of finite general linear and unitary groups
• Fusion systems on a Sylow \(p\)-subgroup of \(G_2(p^n)\) or \(PSU_4(p^n)\)
• Block-exoticity of a family of exotic fusion systems
• A family of fusion systems related to the groups \(\mathrm{Sp}_4(p^a)\) and \(\mathrm G_2(p^a)\).
• A reduction theorem for fusion systems of blocks.
• The Solomon system \({\mathcal F}_{\text{Sol}}(3)\) does not occur as fusion system of a 2-block.
• All 𝑝-local finite groups of rank two for odd prime 𝑝
• Character Table and Blocks of Finite Simple Triality Groups 3 D 4 (q)
• Fusion systems on maximal class 3-groups of rank two revisited
• Die unipotenten charaktere von ²F₄(q²)