It\^{o}'s theorem and monomial Brauer characters

Xiaoyou Chen; Mark L. Lewis

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arXiv · 1703.02452

It\^{o}'s theorem and monomial Brauer characters

Xiaoyou Chen·Mark L. Lewis

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Abstract

Let $G$ be a finite solvable group, and let $p$ be a prime. In this note, we prove that $p$ does not divide $\varphi(1)$ for every irreducible monomial $p$-Brauer character $\varphi$ of $G$ if and only if $G$ has a normal Sylow $p$-subgroup.

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Xiaoyou Chen, Mark L. Lewis. 2017-03-07. It\^{o}'s theorem and monomial Brauer characters. https://arxiv.org/abs/1703.02452

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