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AN ANALOGUE OF HUPPERT’S CONJECTURE FOR CHARACTER CODEGREES
Published online by Cambridge University Press: 08 February 2021
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.
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- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 104 , Issue 2 , October 2021 , pp. 278 - 286
- Copyright
- © 2021 Australian Mathematical Publishing Association Inc.
Footnotes
The research of the second author was in part supported by a grant from IPM (No. 99200028).
References
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