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DEGREES OF BRAUER CHARACTERS AND NORMAL SYLOW $p$-SUBGROUPS

Part of: Representation theory of groups

Published online by Cambridge University Press:  08 January 2020

XIAOYOU CHEN Open the ORCID record for XIAOYOU CHEN [Opens in a new window]  and
MARK L. LEWIS Open the ORCID record for MARK L. LEWIS [Opens in a new window]
XIAOYOU CHEN
Affiliation:
College of Science, Henan University of Technology, Zhengzhou450001, China email cxymathematics@hotmail.com
MARK L. LEWIS*
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA email lewis@math.kent.edu
*
✉lewis@math.kent.edu
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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 $G$.

Keywords

Brauer charactermonomial charactercharacter degreeSylow subgroup

MSC classification

Primary: 20C20: Modular representations and characters
Secondary: 20C15: Ordinary representations and characters
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 102 , Issue 2 , October 2020 , pp. 237 - 239
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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References

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