Brauer’s height zero conjecture for two primes

Abstract

Let p and q be two primes. We propose that Brauer’s Height Zero Conjecture for the principal p-blocks of finite groups can naturally be extended from the perspective of q. We prove one direction of this new conjecture, and show the reverse direction assuming that the Inductive Alperin–McKay condition holds for the finite simple groups.

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Correspondence to Gabriel Navarro.

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Gunter Malle gratefully acknowledges financial support by SFB TRR 195. The research of Gabriel Navarro is supported by MTM2016-76196-P and FEDER funds. He also thanks B. Späth for some discussions on Theorem 2.1.

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Malle, G., Navarro, G. Brauer’s height zero conjecture for two primes. Math. Z. 295, 1723–1732 (2020). https://doi.org/10.1007/s00209-019-02422-6

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Keyword

  • Brauer’s Height Zero Conjecture

Mathematics Subject Classification

  • Primary 20C15