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SQUARES OF DEGREES OF BRAUER CHARACTERS AND MONOMIAL BRAUER CHARACTERS
Published online by Cambridge University Press: 29 January 2019
Abstract
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 $G$.
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- Research Article
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- Copyright
- © 2019 Australian Mathematical Publishing Association Inc.
Footnotes
The first author acknowledges the hospitality of the Department of Mathematical Sciences of Kent State University and the support of the China Scholarship Council, the Program for Young Key Teachers of Henan University of Technology, the Project of Foreign Experts Affairs of Henan Province, Funds of Henan University of Technology (2014JCYJ14, 26510009), Project of Department of Education of Henan Province (17A110004), Fund of Henan Province (162300410066) and the NSFC (11571129, 11771356, 11601121, 11701149).
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