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arXiv · 2010.07631

Linear characters of Sylow subgroups of symmetric groups

Eugenio Giannelli·Stacey Law·Jason Long
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Abstract

Let $p$ be any prime. Let $P_n$ be a Sylow $p$-subgroup of the symmetric group $S_n$. Let $ϕ$ and $ψ$ be linear characters of $P_n$ and let $N$ be the normaliser of $P_n$ in $S_n$. In this article we show that the inductions of $ϕ$ and $ψ$ to $S_n$ are equal if, and only if, $ϕ$ and $ψ$ are $N$--conjugate. This is an analogue for symmetric groups of a result of Navarro for $p$-solvable groups.

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Eugenio Giannelli, Stacey Law, Jason Long. 2021-06-24. Linear characters of Sylow subgroups of symmetric groups. https://arxiv.org/abs/2010.07631

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