Height Zero Conjecture with Galois Automorphisms

2022/09/19 by Malle, Gunter, Navarro, Gabriel · 2 citations
#20C15 #20C33 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2209.08798

Abstract

We prove a strengthening of Brauer's height zero conjecture for principal 2-blocks with Galois automorphisms. This requires a new extension of the Itô--Michler theorem for the prime~2, again with Galois automorphisms. We close, this time for odd primes p, with a new characterisation of p-closed groups via the decomposition numbers of certain characters.

Cited by

• Height zero characters and Galois automorphisms
• Principal blocks, irreducible restriction, fields and degrees

Related

• Height zero characters and Galois automorphisms
• A Brauer--Galois height zero conjecture
• A normal version of Brauer's height zero conjecture
• Brauer's Height Zero Conjecture for Principal Blocks
• On the projective height zero conjecture