Orbit sizes, character degrees and Sylow subgroups.

DOI10.1016/S0001-8708(03)00093-8zbMath1068.20008MaRDI QIDQ1826873

Alexander Moretó, Thomas R. Wolf

Publication date: 6 August 2004

Published in: Advances in Mathematics (Search for Journal in Brave)

zbMATH Keywords

nilpotent groupsSylow subgroupscharacter degreesderived lengthsFitting subgroupheight-zero conjecturetransitive solvable permutation groupszeroes of characters

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Ordinary representations and characters (20C15) Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Arithmetic and combinatorial problems involving abstract finite groups (20D60)

Related Items (42)

Orbits of the Actions of Odd-Order Solvable Groups ⋮ Abelian quotients and orbit sizes of solvable linear groups ⋮ On the number of conjugacy classes of zeros of characters. ⋮ Large character degrees of solvable groups with Abelian Sylow 2-subgroups. ⋮ Kernels of \(p'\)-degree irreducible characters ⋮ Fitting height and character degree graphs. ⋮ Landau's theorem and the number of conjugacy classes of zeros of characters ⋮ Blocks of small defect in alternating groups and squares of Brauer character degrees ⋮ The prime-power hypothesis and solvable groups ⋮ Variants of some of the Brauer-Fowler theorems ⋮ Methods and questions in character degrees of finite groups ⋮ \(p\)-parts of character degrees and the index of the Fitting subgroup. ⋮ Arithmetical conditions of orbit sizes of linear groups of odd order ⋮ Monomial characters and the index of the Fitting subgroup of a solvable group ⋮ The average character degree of finite groups and Gluck's conjecture ⋮ On \(p\)-parts of Brauer character degrees and \(p\)-regular conjugacy class sizes of finite groups ⋮ Large orbit sizes in finite group actions ⋮ On the largest Brauer and \(p^\prime\)-character degrees ⋮ Large orbits of odd-order subgroups of solvable linear groups. ⋮ On Gluck's conjecture ⋮ Monomial characters of finite solvable groups ⋮ On the number of conjugacy classes of zeros of characters and the length of solvable groups ⋮ On Large Orbits of Actions of Finite Soluble Groups: Applications ⋮ On \(p\)-parts of character degrees and conjugacy class sizes of finite groups ⋮ Group actions and non-vanishing elements in solvable groups ⋮ Bounding the Diameter of the Brauer Graph of a Block of a Solvable Group ⋮ Base sizes for primitive groups with soluble stabilisers ⋮ The size of the largest conjugacy classes and the Sylow \(p\)-subgroups of finite groups ⋮ Bounding an Index by the Largest Character Degree of ap-Solvable Group ⋮ Controlling composition factors of a finite group by its character degree ratio. ⋮ Regular orbits of finite primitive solvable groups ⋮ A variation on theorems of Jordan and Gluck. ⋮ Large orbits of \(p\)-groups on characters and applications to character degrees. ⋮ Every coprime linear group admits a base of size two ⋮ Character degrees, conjugacy class sizes, and element orders: three primes ⋮ Orbit sizes and odd order composition factors of finite linear groups ⋮ Abelian subgroups, nilpotent subgroups, and the largest character degree of a finite group ⋮ Orbits of the actions of finite solvable groups. ⋮ Large character degrees of solvable 3’-groups ⋮ On large orbits of subgroups of linear groups ⋮ On a conjecture of Gluck. ⋮ Blocks of small defect.

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