2024/02/13 by Malle, Gunter, Moretó, Alexander, Rizo, Noelia +1 · 2 citations
#20C15 #20C20 #20C33 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2402.08361
Recently, Malle and Navarro obtained a Galois strengthening of Brauer's height zero conjecture for principal p-blocks when p=2, considering a particular Galois automorphism of order~2. In this paper, for any prime p we consider a certain elementary abelian p-subgroup of the absolute Galois group and propose a Galois version of Brauer's height zero conjecture for principal p-blocks. We prove it when p=2 and also for arbitrary p when G does not involve certain groups of Lie type of small rank as composition factors. Furthermore, we prove it for almost simple groups and for p-solvable groups.