On \({p} \)-parts of character codegrees (Q1983954)
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scientific article; zbMATH DE number 7394412
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On \({p} \)-parts of character codegrees |
scientific article; zbMATH DE number 7394412 |
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On \({p} \)-parts of character codegrees (English)
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13 September 2021
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Let \(G\) be a finite group. For an irreducible character \(\chi\) of \(G\), its codegree has been defined by \(\mathrm{cod}(\chi)=|G:\mathrm{ker} \chi|/\chi(1)\). In this paper, for a given prime \(p\), the authors show that \(|G/O_{p'p}(G)|_p\leq p^{c_p(G)}\) where \(c_p(G)=\max \{\log_p (\mathrm{cod}(\chi))_p| \chi\in \mathrm{Irr}(G) \}\) and characterize the finite groups \(G\) with \(c_p(G)\leq 1\).
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finite groups
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character codegree
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\({p} \)-solvable groups
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