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SQUARES OF DEGREES OF BRAUER CHARACTERS AND MONOMIAL BRAUER CHARACTERS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 100 / Issue 1 / August 2019
- Published online by Cambridge University Press:
- 29 January 2019, pp. 58-60
- Print publication:
- August 2019
-
- Article
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- You have access
- Export citation
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Let
$G$ be a finite group and let 
$p$ be a prime factor of 
$|G|$. Suppose that 
$G$ is solvable and 
$P$ is a Sylow 
$p$-subgroup of 
$G$. In this note, we prove that 
$P{\vartriangleleft}G$ and 
$G/P$ is nilpotent if and only if 
$\unicode[STIX]{x1D711}(1)^{2}$ divides 
$|G:\ker \unicode[STIX]{x1D711}|$ for all irreducible monomial 
$p$-Brauer characters 
$\unicode[STIX]{x1D711}$ of 
$G$.
