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math.GR2025
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 …
math.RT2025
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…
math.RT2025
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…