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Notes on the largest irreducible character degree of a finite group


Author: Qian Guohua
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1899-1903
MSC (2000): Primary 20C15
DOI: https://doi.org/10.1090/S0002-9939-04-07316-2
Published electronically: January 23, 2004
MathSciNet review: 2053959
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Abstract: Let $G$ be a finite group and $b(G)$ the largest irreducible character degree of $G$. In this note, we show the following results: if $b(G)<p^2$, then $\vert G:O_p(G)\vert _p\leq p$ ; if $b(G)<p^m$ and, in addition, $G$ is $p$-solvable with abelian Sylow $p$-subgroup, then $ \vert G:O_p(G)\vert _p< p^m$.


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Additional Information

Qian Guohua
Affiliation: Department of Mathematics, Changshu College, Changshu, Jiansu, 215500, People’s Republic of China
Email: ghqian2000@yahoo.com.cn

DOI: https://doi.org/10.1090/S0002-9939-04-07316-2
Keywords: Finite group, character degree
Received by editor(s): January 28, 2003
Received by editor(s) in revised form: April 3, 2003
Published electronically: January 23, 2004
Additional Notes: Project supported by the National Nature Science Foundation of China and the Nature Science Foundation of Jiangsu Provincial Education Department (03KJB11002).
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2004 American Mathematical Society