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AN ANALOGUE OF HUPPERT’S CONJECTURE FOR CHARACTER CODEGREES

Part of: Representation theory of groups Graph theory

Published online by Cambridge University Press:  08 February 2021

A. BAHRI Open the ORCID record for A. BAHRI [Opens in a new window] ,
Z. AKHLAGHI Open the ORCID record for Z. AKHLAGHI [Opens in a new window]  and
B. KHOSRAVI Open the ORCID record for B. KHOSRAVI [Opens in a new window]
A. BAHRI
Affiliation:
Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 15914Tehran, Iran e-mail: afsanebahri@aut.ac.ir
Z. AKHLAGHI*
Affiliation:
Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 15914Tehran, Iran and School of Mathematics, Institute for Research in Fundamental Science (IPM), PO Box 19395-5746, Tehran, Iran
B. KHOSRAVI
Affiliation:
Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 15914 Tehran, Iran e-mail: khosravibbb@yahoo.com
*
e-mail: z_akhlaghi@aut.ac.ir
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Abstract

Let G be a finite group, let ${\mathrm{Irr}}(G)$ be the set of all irreducible complex characters of G and let $\chi \in {\mathrm{Irr}}(G)$ . Define the codegrees, ${\mathrm{cod}}(\chi ) = |G: {\mathrm{ker}}\chi |/\chi (1)$ and ${\mathrm{cod}}(G) = \{{\mathrm{cod}}(\chi ) \mid \chi \in {\mathrm{Irr}}(G)\} $ . We show that the simple group ${\mathrm{PSL}}(2,q)$ , for a prime power $q>3$ , is uniquely determined by the set of its codegrees.

Keywords

characterisationcodegreesimple group

MSC classification

Primary: 20C15: Ordinary representations and characters
Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 104 , Issue 2 , October 2021 , pp. 278 - 286
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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Footnotes

The research of the second author was in part supported by a grant from IPM (No. 99200028).

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