#### Vol. 8, No. 8, 2014

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McKay natural correspondences on characters

### Gabriel Navarro, Pham Huu Tiep and Carolina Vallejo

Vol. 8 (2014), No. 8, 1839–1856
##### Abstract

Let $G$ be a finite group, let $p$ be an odd prime, and let $P\in {Syl}_{p}\left(G\right)$. If ${N}_{G}\left(P\right)=P{C}_{G}\left(P\right)$, then there is a canonical correspondence between the irreducible complex characters of $G$ of degree not divisible by $p$ belonging to the principal block of $G$ and the linear characters of $P$. As a consequence, we give a characterization of finite groups that possess a self-normalizing Sylow $p$-subgroup or a $p$-decomposable Sylow normalizer.

##### Keywords
McKay conjecture, self-normalizing Sylow subgroup, $p$-decomposable Sylow normalizer
Primary: 20C15
Secondary: 20C20