arXiv Open Access 2021

Sylow branching coefficients and a conjecture of Malle and Navarro

Eugenio Giannelli Stacey Law Jason Long Carolina Vallejo

Lihat Sumber

Abstrak

We prove that a finite group $G$ has a normal Sylow $p$-subgroup $P$ if, and only if, every irreducible character of $G$ appearing in the permutation character $({\bf 1}_P)^G$ with multiplicity coprime to $p$ has degree coprime to $p$. This confirms a prediction by Malle and Navarro from 2012. Our proof of the above result depends on a reduction to simple groups and ultimately on a combinatorial analysis of the properties of Sylow branching coefficients for symmetric groups.

Topik & Kata Kunci

math.RT math.CO math.GR

Penulis (4)

Eugenio Giannelli

Stacey Law

Jason Long

Carolina Vallejo

Format Sitasi

APA MLA BibTeX

Giannelli, E., Law, S., Long, J., Vallejo, C. (2021). Sylow branching coefficients and a conjecture of Malle and Navarro. https://arxiv.org/abs/2102.06784

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2021
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓