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A NOTE ON $p$-PARTS OF BRAUER CHARACTER DEGREES

Part of: Representation theory of groups

Published online by Cambridge University Press:  06 May 2020

JINBAO LI Open the ORCID record for JINBAO LI [Opens in a new window]  and
YONG YANG Open the ORCID record for YONG YANG [Opens in a new window]
JINBAO LI
Affiliation:
Key Laboratory of Group and Graph Theories and Applications,Chongqing University of Arts and Sciences, Chongqing402160, PR China email leejinbao25@163.com
YONG YANG*
Affiliation:
Department of Mathematics,Texas State University, 601 University Drive,San Marcos, TX78666, USA email yang@txstate.edu
*
✉yang@txstate.edu
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Abstract

Let $G$ be a finite group and $p$ be an odd prime. We show that if $\mathbf{O}_{p}(G)=1$ and $p^{2}$ does not divide every irreducible $p$-Brauer character degree of $G$, then $|G|_{p}$ is bounded by $p^{3}$ when $p\geqslant 5$ or $p=3$ and $\mathsf{A}_{7}$ is not involved in $G$, and by $3^{4}$ if $p=3$ and $\mathsf{A}_{7}$ is involved in $G$.

Keywords

finite groupsBrauer charactercharacter degreep-part

MSC classification

Primary: 20C15: Ordinary representations and characters
Secondary: 20C20: Modular representations and characters 20D05: Finite simple groups and their classification

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 1 , February 2021 , pp. 83 - 87
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

The project was supported by NSFC (11671063), the Natural Science Foundation of CSTC (cstc2018jcyjAX0060) and a grant from the Simons Foundation (No. 499532).

References

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