Abelian quotients and orbit sizes of solvable linear groups

DOI10.1007/s11856-015-1259-4zbMath1353.20007OpenAlexW2288607629MaRDI QIDQ273072

Thomas Michael Keller, Yong Yang

Publication date: 21 April 2016

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11856-015-1259-4

zbMATH Keywords

irreducible modulesabelian finite groupscharacter of finite groupsnilpotent finite groupsregular orbitrepresentation theory of finite groups

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Modular representations and characters (20C20) Finite abelian groups (20K01) Finite nilpotent groups, (p)-groups (20D15)

Related Items

Abelian quotient of subgroups of solvable linear groups, Class 2 quotients of solvable linear groups, Orbit sizes and the central product group of order 16, Abelian quotients and orbit sizes of linear groups, Large orbit sizes in finite group actions, On the average codegree of a finite group, Linear group actions with at most three orbits of the largest size, Orbit sizes and the dihedral group of order eight, On large orbits of supersoluble subgroups of linear groups, Permutation characters in finite solvable groups, On class 2 quotients of linear groups, Orbits of finite solvable groups on characters., Cartan matrices and Brauer's \(k(B)\)-conjecture. III., On nilpotent group actions on the characters of solvable groups

Cites Work

• Unnamed Item
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• On the maximal subgroups of the finite classical groups
• Orbits of the actions of finite solvable groups.
• The existence of regular orbits for nilpotent groups
• Character theory of finite groups
• Large orbits of \(p\)-groups on characters and applications to character degrees.
• On Brauer's \(k(B)\)-problem
• Orbit sizes, character degrees and Sylow subgroups.
• Bases of primitive linear groups.
• Large orbits of subgroups of solvable linear groups.
• Orbits of finite solvable groups on characters.
• A replacement theorem for \(p\)-groups and a conjecture
• Derived length and conjugacy class sizes.
• Orbit sizes and character degrees, III
• Blocks with equal height zero degrees
• Commutators and the Commutator Subgroup
• On Abelian Quotients of Primitive Groups
• Endliche Gruppen I