Reduced fusion systems over 2-groups of small order

DOI10.1016/j.jalgebra.2017.06.016zbMath1421.20005arXiv1606.05059OpenAlexW2964037731WikidataQ59756014 ScholiaQ59756014MaRDI QIDQ1682045

Joana Ventura, Kasper K. S. Andersen, Robert Oliver

Publication date: 28 November 2017

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

Full work available at URL: https://arxiv.org/abs/1606.05059

zbMATH Keywords

finite simple groupsSylow subgroupsfusion

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Classifying spaces of groups and (H)-spaces in algebraic topology (55R35) Finite simple groups and their classification (20D05)

Related Items

Fusion systems with Benson-Solomon components ⋮ Automorphisms of fusion systems of finite simple groups of Lie typeandAutomorphisms of fusion systems of sporadic simple groups ⋮ Complexity and cohomology of cohomological Mackey functors. ⋮ Fusion systems ⋮ Algorithms for fusion systems with applications to 𝑝-groups of small order

Uses Software

• GAP
• Magma

Cites Work

• Fusion systems and amalgams.
• Strongly closed subgroups of finite groups.
• Errata: Evidence for a new finite simple group
• Strongly closed 2-subgroups of finite groups
• Finite groups with Sylow 2-subgroups of type \(\Omega(7,q)\), \(q\equiv\pm 3 (\mod B)\)
• The subgroups of \(PSL(5,2^a)\)
• The Magma algebra system. I: The user language
• 2-fusion in finite groups
• Homotopy equivalences of \(p\)-completed classifying spaces of finite groups
• Solvability of groups of odd order
• Frobenius categories.
• A simple group of order 44,352,000
• The characterization of finite groups with dihedral Sylow 2-subgroups. I, II
• Computation of characters of the Higman-Sims group and its automorphism group
• Transitive Gruppen gerader Ordnung, in denen jede Involution genau einen Punkt fest läßt
• Finite groups with Sylow 2-subgroups of type \({\mathfrak U}_{12}\)
• Reduced, tame and exotic fusion systems
• The generalized Fitting subsystem of a fusion system
• Equivalences between fusion systems of finite groups of Lie type
• A characterization of finite groups containing a strongly closed 2-subgroup
• Extensions of $p$-local finite groups
• Reduced fusion systems over 2-groups of sectional rank at most 4
• Saturated fusion systems over $2$-groups
• Some Evidence for the Existence of a New Simple Group
• Two New Constructions of the O'Nan Group
• The homotopy theory of fusion systems
• Splitting fusion systems over 2-groups
• Automorphisms of fusion systems of finite simple groups of Lie typeandAutomorphisms of fusion systems of sporadic simple groups
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item