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ON ANALOGUES OF HUPPERT’S CONJECTURE

Part of: Representation theory of groups

Published online by Cambridge University Press:  18 January 2021

YONG YANG Open the ORCID record for YONG YANG [Opens in a new window]
YONG YANG*
Affiliation:
Key Laboratory of Group and Graph Theories and Applications, Chongqing University of Arts and Sciences, Chongqing, China and Department of Mathematics, Texas State University, 601 University Drive, San Marcos, TX 78666, USA
*
e-mail: [email protected]
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Abstract

Let G be a finite group and $\chi $ be a character of G. The codegree of $\chi $ is ${{\operatorname{codeg}}} (\chi ) ={|G: \ker \chi |}/{\chi (1)}$ . We write $\pi (G)$ for the set of prime divisors of $|G|$ , $\pi ({{\operatorname{codeg}}} (\chi ))$ for the set of prime divisors of ${{\operatorname{codeg}}} (\chi )$ and $\sigma ({{\operatorname{codeg}}} (G))= \max \{|\pi ({{\operatorname{codeg}}} (\chi ))| : \chi \in {\textrm {Irr}}(G)\}$ . We show that $|\pi (G)| \leq ({23}/{3}) \sigma ({{\operatorname{codeg}}} (G))$ . This improves the main result of Yang and Qian [‘The analog of Huppert’s conjecture on character codegrees’, J. Algebra478 (2017), 215–219].

Keywords

charactercodegreefinite group

MSC classification

Primary: 20C15: Ordinary representations and characters
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 104 , Issue 2 , October 2021 , pp. 272 - 277
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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Footnotes

This work was partially supported by the NSF of China (No. 11671063) and a grant from the Simons Foundation (No. 499532).

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