The largest Irreducible Character Degree of a Finite Group

DOI10.4153/CJM-1985-026-8zbMath0572.20004MaRDI QIDQ3689345

David Gluck

Publication date: 1985

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

zbMATH Keywords

faithful irreducible characterssolvable groupsirreducible character degreesFrobenius reciprocityclassification of simple groupslargest normal Abelian subgroup

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) 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)

Related Items (29)

Large character degrees of solvable groups with Abelian Sylow 2-subgroups. ⋮ The character degree ratio and large abelian subgroups ⋮ On the number of prime divisors of character degrees and conjugacy classes of a finite group ⋮ Unnamed Item ⋮ Variants of some of the Brauer-Fowler theorems ⋮ Arithmetical conditions of orbit sizes of linear groups of odd order ⋮ The average character degree of finite groups and Gluck's conjecture ⋮ A variation on a theorem of Gluck ⋮ Large orbit sizes in finite group actions ⋮ On the largest Brauer and \(p^\prime\)-character degrees ⋮ Irreducible characters of even degree and normal Sylow 2-subgroups ⋮ Large orbits of odd-order subgroups of solvable linear groups. ⋮ On Gluck's conjecture ⋮ Monomial characters of finite solvable groups ⋮ On Large Orbits of Actions of Finite Soluble Groups: Applications ⋮ BOUNDING THE NUMBER OF IRREDUCIBLE CHARACTER DEGREES OF A FINITE GROUP IN TERMS OF THE LARGEST DEGREE ⋮ 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. ⋮ On group gradings on PI-algebras. ⋮ Large orbits of subgroups of solvable linear groups. ⋮ A variation on theorems of Jordan and Gluck. ⋮ Finite groups with an irreducible character of large degree. ⋮ Orbit sizes and odd order composition factors of finite linear groups ⋮ Abelian subgroups, nilpotent subgroups, and the largest character degree of a finite group ⋮ Large character degrees of solvable 3’-groups ⋮ On large orbits of subgroups of linear groups ⋮ Orbit sizes, character degrees and Sylow subgroups. ⋮ On a conjecture of Gluck.

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