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SQUARES OF DEGREES OF BRAUER CHARACTERS AND MONOMIAL BRAUER CHARACTERS

Published online by Cambridge University Press:  29 January 2019

XIAOYOU CHEN
Affiliation:
College of Science, Henan University of Technology, Zhengzhou 450001, China email [email protected]
MARK L. LEWIS*
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA email [email protected]
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Abstract

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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 $G$.

Type
Research Article
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).

References

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