Solvable groups whose monomial, monolithic characters have prime power codegrees

Chen, Xiaoyou; Lewis, Mark L.

doi:10.22108/ijgt.2022.131101.1755

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	Solvable groups whose monomial, monolithic characters have prime power codegrees
International Journal of Group Theory
مقاله 1، دوره 12، شماره 4، اسفند 2023، صفحه 223-226 اصل مقاله (351.08 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2022.131101.1755
نویسندگان
Xiaoyou Chen^* ¹؛ Mark L. Lewis²
¹School of Sciences, Henan University of Technology, P.O.Box 450001, Zhengzhou, China
²Department of Mathematical Sciences, Kent State University, P.O.Box 44242, Kent, USA
چکیده
In this note, we prove that if $G$ is solvable and ${\rm cod}(\chi)$ is a $p$-power for every nonlinear, monomial, monolithic $\chi\in {\rm Irr}(G)$ or every nonlinear, monomial, monolithic $\chi \in {\rm IBr} (G)$, then $P$ is normal in $G$, where $p$ is a prime and $P$ is a Sylow $p$-subgroup of $G$.
کلیدواژه‌ها
monomial Characters؛ monolithic characters؛ character codegrees

مراجع
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Solvable groups whose monomial, monolithic characters have prime power codegrees