Some generalized characters (Q1911331)
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scientific article; zbMATH DE number 868025
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some generalized characters |
scientific article; zbMATH DE number 868025 |
Statements
Some generalized characters (English)
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9 June 1996
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If \(G\) is a finite group and \(p\) is a prime, define \(\chi_p\colon G\to\mathbb{Z}\) by setting, for \(g\in G\), \[ \chi_p(g)=|\{h\in G\mid\text{the Sylow \(p\)-subgroups of }\langle g,h\rangle\text{ are Abelian}\}|. \] The object of this note is to prove that \(\chi_p\) is a generalized character.
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Sylow subgroups
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finite groups
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generalized characters
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