Characters and Sylow $3$-subgroup abelianization

Fuente: arXiv
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Hauptverfasser: Giannelli, Eugenio, Rizo, Noelia, Fry, A. A. Schaeffer, Vallejo, Carolina
Format: Preprint
Veröffentlicht: 2024
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author Giannelli, Eugenio
Rizo, Noelia
Fry, A. A. Schaeffer
Vallejo, Carolina
author_facet Giannelli, Eugenio
Rizo, Noelia
Fry, A. A. Schaeffer
Vallejo, Carolina
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2405_16665
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Characters and Sylow $3$-subgroup abelianization
Giannelli, Eugenio
Rizo, Noelia
Fry, A. A. Schaeffer
Vallejo, Carolina
Group Theory
Representation Theory
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.
title Characters and Sylow $3$-subgroup abelianization
topic Group Theory
Representation Theory
url https://arxiv.org/abs/2405.16665