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DEGREES OF BRAUER CHARACTERS AND NORMAL SYLOW
$p$-SUBGROUPS
Published online by Cambridge University Press: 08 January 2020
Abstract
Let $p$ be a prime,
$G$ a solvable group and
$P$ a Sylow
$p$-subgroup of
$G$. We prove that
$P$ is normal in
$G$ if and only if
$\unicode[STIX]{x1D711}(1)_{p}^{2}$ divides
$|G:\ker (\unicode[STIX]{x1D711})|_{p}$ for all monomial monolithic irreducible
$p$-Brauer characters
$\unicode[STIX]{x1D711}$ of
$G$.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 102 , Issue 2 , October 2020 , pp. 237 - 239
- Copyright
- © 2020 Australian Mathematical Publishing Association Inc.
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