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Height Zero Conjecture with Galois Automorphisms (2209.08798v1)
Published 19 Sep 2022 in math.RT and math.GR
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 It^o--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.
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