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Sylow branching coefficients and a conjecture of Malle and Navarro

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 نشر من قبل Stacey Law
 تاريخ النشر 2021
  مجال البحث
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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.



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