Characters and Sylow $3$-subgroup abelianization
Group Theory
2024-07-16 v2 Representation Theory
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.
Cite
@article{arxiv.2405.16665,
title = {Characters and Sylow $3$-subgroup abelianization},
author = {Eugenio Giannelli and Noelia Rizo and A. A. Schaeffer Fry and Carolina Vallejo},
journal= {arXiv preprint arXiv:2405.16665},
year = {2024}
}
Comments
slight title change and other minor changes, following helpful comments thanks to Gunter Malle and Bejamin Sambale