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arXiv · 2405.16665

Characters and Sylow $3$-subgroup abelianization

Eugenio Giannelli·Noelia Rizo·A. A. Schaeffer Fry·Carolina Vallejo
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Abstract

We characterize when a finite group G possesses a Sylow 3-subgroup P with abelianization of order 9 in terms of the number of height zero characters lying in the principal 3-block of G, settling a conjecture put forward by Navarro, Sambale, and Tiep in 2018. Along the way, we show that a recent result by Laradji on the number of character of height zero in a block that lie above a given character of some normal subgroup holds, without any hypothesis on the group for blocks of maximal defect.

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Eugenio Giannelli, Noelia Rizo, A. A. Schaeffer Fry, Carolina Vallejo. 2024-05-26. Characters and Sylow $3$-subgroup abelianization. https://arxiv.org/abs/2405.16665

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