On minimal positive heights for blocks of almost quasi-simple groups

2024/10/30 by Gunter Malle, Malle, Gunter, A. A. Schaeffer Fry +1 · 1 citation
Mathematics · #20C15 #20C20 #20C33 #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2410.22745

openalex publication_date 2024/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Eaton--Moretó conjecture extends the recently-proven Brauer height zero conjecture to blocks with non-abelian defect group, positing equality between the minimal positive heights of a block of a finite group and its defect group. Here we provide further evidence for the inequality in this conjecture that is not implied by Dade's conjecture. Specifically, we consider minimal counter-examples and show that these cannot be found among almost quasi-simple groups for p≥5. Along the way, we observe that most such blocks have minimal positive height equal to~1.

Cited by

• Sylow subgroups and the number of irreducible characters of degrees divisible by a prime p

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• Characters of positive height in blocks of finite quasi-simple groups
• Minimal heights and defect groups with two character degrees
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• Brauer's height zero conjecture for quasi-simple goups
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