Characters and Sylow 3-subgroup abelianization

2024/05/26 by Eugenio Giannelli, Noelia Rizo, Giannelli, Eugenio +5 · 1 citation
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2405.16665

openalex publication_date 2024/05/26 · openalex created_date 2024/05/29 · openalex updated_date 2026/07/28

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.

Cited by

• Characters and the Generation of Sylow 3-Subgroups For Almost Simple Groups

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