Sylow branching coefficients and a conjecture of Malle and Navarro

2021/02/12 by Eugenio Giannelli, Giannelli, Eugenio, Stacey Law +5 · 1 citation
Computer Science · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Limits and Structures in Graph Theory #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2102.06784

openalex publication_date 2021/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• The Moretó-Rizo conjectures for symmetric groups

Related

• The continuity of p-rationality and a lower bound for p'-degree characters of finite groups
• Minimal numbers of linear constituents in Sylow restrictions for symmetric groups
• Sylow branching trees for symmetric groups
• Character correspondeces in solvable groups with a self-normalizing Sylow subgroup
• A note on restriction of Characters of Alternating groups to Sylow\n Subgroups