A solvable version of the Baer–Suzuki theorem

DOI10.1090/S0002-9947-2010-04932-3zbMath1214.20025arXiv0902.1738OpenAlexW2048813750MaRDI QIDQ3056574

Simon D. Guest

Publication date: 12 November 2010

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

Full work available at URL: https://arxiv.org/abs/0902.1738

zbMATH Keywords

soluble groupsfinite groupsnilpotent groupssimple groupsBaer-Suzuki theorem

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Special subgroups (Frattini, Fitting, etc.) (20D25) Generators, relations, and presentations of groups (20F05) Finite simple groups and their classification (20D05)

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Uses Software

• Magma
• CHEVIE
• ATLAS Group Representations

Cites Work

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• Some applications of the first cohomology group
• A description of Baer-Suzuki type of the solvable radical of a finite group.
• The root subgroups for maximal tori in finite groups of Lie type
• The maximal subgroups of the Steinberg triality groups \(3D_ 4(q)\) and their automorphism groups
• The maximal subgroups of the Chevalley groups \(G_ 2(q)\) with q odd, the Ree groups \(2G_ 2(q)\), and their automorphism groups
• The conjugate classes of unipotent elements of the Chevalley groups \(E_ 7\) and \(E_ 8\).
• The Magma algebra system. I: The user language
• Generation of finite almost simple groups by conjugates.
• Probabilistic generation of finite simple groups
• CHEVIE -- A system for computing and processing generic character tables
• The maximal subgroups of \({}^ 2F_ 4(q^ 2)\)
• A commutator description of the solvable radical of a finite group.
• ANATOMY OF THE MONSTER: II
• Characterizations of the solvable radical
• The local structure of finite groups of characteristic 2 type
• Subgroups of Maximal Rank in Finite Exceptional Groups of Lie Type
• Subgroups of Algebraic Groups Containing Regular Unipotent Elements
• Linear Groups with Orders Having Certain Large Prime Divisors
• Fixed point spaces in actions of classical algebraic groups
• Jordan block sizes of unipotent elements in exceptional algebraic groups
• Factorizations of simple algebraic groups
• BURNSIDE-TYPE PROBLEMS RELATED TO SOLVABILITY
• On Ree's Series of Simple Groups
• Nonsolvable finite groups all of whose local subgroups are solvable
• On the conjugacy classes in the unitary, symplectic and orthogonal groups
• On a class of doubly transitive groups