10 papers
On -blocks with quaternion defect groups
Charles Eaton, Florian Eisele, Radha Kessar +2
We determine the Morita equivalence classes of -blocks with quaternion defect groups of arbitrary -power order, thereby completing the proof of Donovan's conjecture for block…
Galois automorphisms and blocks covering unipotent blocks
L. Ruhstorfer, A. A. Schaeffer Fry
In this paper we prove that a recent condition of Lyons--Martínez--Navarro--Tiep, regarding the field of values of extensions of characters in principal blocks, is satisfied for al…
Galois action on the principal block and generation of Sylow 3-subgroups
Eden Ketchum, J. Miquel Martínez, Noelia Rizo +1
In this paper, we prove one direction of a conjecture of Navarro-Rizo-Schaeffer Fry-Vallejo positing an algorithm to determine from the character table whether a finite group has $…
Sylow subgroups and the number of irreducible characters of degrees divisible by a prime
James P. Cossey, Mark L. Lewis, A. A. Schaeffer Fry +1
Let be a finite group and a prime. We establish an upper bound for the derived length of a Sylow -subgroup of in terms of the number of irreducible characters of …
The Picky Conjecture for groups of Lie type
Gunter Malle, A. A. Schaeffer Fry
Recently, Moretó and Rizo proposed a conjecture, known as the Picky Conjecture, proposing new character correspondences extending the McKay Conjecture. We prove the Picky Conjectur…
The Isaacs--Navarro Galois conjecture
L. Ruhstorfer, A. A. Schaeffer Fry
We prove the original Galois refinement of the McKay conjecture, proposed by Isaacs--Navarro in 2002, providing an important subcase of the celebrated McKay--Navarro conjecture wit…
The -rationality of height-zero characters
Nguyen N. Hung, A. A. Schaeffer Fry
We propose and present evidence for a conjectural global-local phenomenon concerning the -rationality of -height-zero characters. Specifically, if is a height-zero charac…
On minimal positive heights for blocks of almost quasi-simple groups
Gunter Malle, A. A. Schaeffer Fry
The Eaton--Moretó conjecture extends the recently-proven Brauer height zero conjecture to blocks with non-abelian defect group, positing equality between the minimal positive heigh…
A Brauer--Galois height zero conjecture
Gunter Malle, Alexander Moretó, Noelia Rizo +1
Recently, Malle and Navarro obtained a Galois strengthening of Brauer's height zero conjecture for principal -blocks when , considering a particular Galois automorphism of…
Brauer's problem 21 for principal blocks
Alexander Moretó, Noelia Rizo, A. A. Schaeffer Fry
Problem 21 of Brauer's list of problems from 1963 asks whether for any positive integer k there are finitely many isomorphism classes of groups that occur as the defect group of a…