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arXiv · 2410.22745

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

Gunter Malle·A. A. Schaeffer Fry
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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 $p\ge5$. Along the way, we observe that most such blocks have minimal positive height equal to~1.

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Gunter Malle, A. A. Schaeffer Fry. 2024-10-30. On minimal positive heights for blocks of almost quasi-simple groups. https://arxiv.org/abs/2410.22745

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