Sylow Branching Coefficients and a Conjecture of Malle and Navarro

Abstract: Let $G$ be a finite group and let $P$ be a Sylow subgroup of $G$.

In 2012 Malle and Navarro conjectured that $P$ is normal in $G$ if and only if the permutation character associated to the natural action of $G$ on the cosets of $P$ has some specific structural properties. In recent joint work with Law, Long and Vallejo we prove this conjecture.

We will start this talk by describing the problem and its relevance in the context of representation theory of finite groups.

Then we will introduce and review some recent results on Sylow Branching Coefficients for symmetric groups.

Finally we will talk about the crucial role played by these objects in our proof of the conjecture.

group theory

Audience: researchers in the topic

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GOThIC - Ischia Online Group Theory Conference

Series comments: Please send a message to andrea.caranti@unitn.it to receive a link to the Zoom room where the conference (a series of talks, actually) takes place.

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