# Sylow branching coefficients for symmetric groups

@article{Giannelli2019SylowBC, title={Sylow branching coefficients for symmetric groups}, author={Eugenio Giannelli and Stacey Law}, journal={arXiv: Representation Theory}, year={2019} }

Let $p\ge 5$ be a prime and let $n$ be a natural number. In this article we describe the irreducible constituents of the induced characters $\phi\big\uparrow^{\mathfrak{S}_n}$ for arbitrary linear characters $\phi$ of a Sylow $p$-subgroup of the symmetric group $\mathfrak{S}_n$, generalising earlier results of the authors. By doing so, we introduce Sylow branching coefficients for symmetric groups.

## 3 Citations

Sylow branching coefficients and a conjecture of Malle and Navarro

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We prove that a finite group G has a normal Sylow psubgroup P if, and only if, every irreducible character of G appearing in the permutation character (1P ) G with multiplicity coprime to p has…

On plethysms and Sylow branching coefficients

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We prove a recursive formula for plethysm coefficients of the form a λ,(m) , generalising results on plethysms due to Bruns–Conca–Varbaro and de Boeck–Paget–Wildon. From this we deduce a stability…

Linear characters of Sylow subgroups of symmetric groups.

- Mathematics
- 2020

Let $p$ be any prime. Let $P_n$ be a Sylow $p$-subgroup of the symmetric group $S_n$. Let $\phi$ and $\psi$ be linear characters of $P_n$ and let $N$ be the normaliser of $P_n$ in $S_n$. In this…

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