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arXiv · 1710.01596

Even degree characters in principal blocks

Eugenio Giannelli·Gunter Malle·Carolina Vallejo
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Abstract

We characterise finite groups such that for an odd prime $p$ all the irreducible characters in its principal $p$-block have odd degree. We show that this situation does not occur in non-abelian simple groups of order divisible by $p$ unless $p=7$ and the group is $M_{22}$. As a consequence we deduce that if $p\neq 7$ or if $M_{22}$ is not a composition factor of a group $G$, then the condition above is equivalent to $G/O_{p'}(G)$ having odd order.

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Eugenio Giannelli, Gunter Malle, Carolina Vallejo. 2017-10-04. Even degree characters in principal blocks. https://arxiv.org/abs/1710.01596

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