Concepedia

Prime divisors of irreducible character degrees and of conjugacy class sizes in finite groups

Carlo Casolo, Silvio Dolfi

Journal of Group Theory · 2007 · 19 citations · 8 references

Concepts

Linear BoundsConjugacy ClassRepresentation Theoryρ-σ ConjectureFrattini SubgroupPrime DivisorsGroup RepresentationNilpotent GroupIrreducible Character Degrees

Abstract

We establish linear bounds for the ρ-σ conjecture for irreducible character degrees and conjugacy class sizes of any finite group.

References

8

On the length of the conjugacy classes of finite groups

David Chillag, Marcel Herzog · Journal of Algebra · 1990 · 96 citations

Coxeter Group, Geometric Group Theory, Representation Theory +6

Primitive Groups with no Regular Orbits on the Set of Subsets

Ákos Seress · Bulletin of the London Mathematical Society · 1997 · 67 citations

Coxeter Group, Geometric Group Theory, Permutation Domain +9

Prime Factors of Character Degrees of Solvable Groups

David Gluck, Olaf Manz · Bulletin of the London Mathematical Society · 1987 · 23 citations · Full text

Coxeter Group, Representation Theory, Prime Factors +2

A conjecture about character degrees of solvable groups

David Gluck · Journal of Algebra · 1991 · 16 citations

Solvable Groups, Representation Theory, Frattini Subgroup +2

Arithmetically long orbits of solvable linear groups

Olaf Manz, Thomas R. Wolf · Illinois Journal of Mathematics · 1993 · 13 citations

Coxeter Group, Lie Group, Long Orbits +4