On 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. In this talk we will explain the main ideas involved in the proof. In particular we will discuss the importance of studying Sylow Branching Coefficients in this context.

group theory

Audience: researchers in the topic

Finite Groups in Valencia

Series comments: The seminar meets weekly from February 26th to March 30th 2021.

For a detailed schedule and registration details, please visit the seminar webpage at

sites.google.com/view/finite-groups-seminar2021