Sylow branching coefficients and a conjecture of Malle and Navarro
Publication Date
2021-02-12Journal Title
Bulletin of the London Mathematical Society
ISSN
0024-6093
Publisher
Wiley
Language
en
Type
Article
This Version
AO
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Giannelli, E., Law, S., Long, J., & Vallejo, C. (2021). Sylow branching coefficients and a conjecture of Malle and Navarro. Bulletin of the London Mathematical Society https://doi.org/10.1112/blms.12584
Description
Funder: Emmanuel College, Cambridge
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.
Keywords
20C15, 20C20, 20C30, 20C33, RESEARCH ARTICLE, RESEARCH ARTICLES
Sponsorship
Spanish National Research Council (20205CEX001)
ERC (647678)
Ministerio de Ciencia e Innovación (PID2019‐103854GB‐I00, PID2020‐118193GA‐I00)
Identifiers
blms12584, 2102.06784
External DOI: https://doi.org/10.1112/blms.12584
This record's URL: https://www.repository.cam.ac.uk/handle/1810/335001
Rights
Licence:
http://creativecommons.org/licenses/by-nc/4.0/
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