A characterization of \(\mathcal N\)-constrained groups. (Q1880179)
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scientific article; zbMATH DE number 2101531
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A characterization of \(\mathcal N\)-constrained groups. |
scientific article; zbMATH DE number 2101531 |
Statements
A characterization of \(\mathcal N\)-constrained groups. (English)
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22 September 2004
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Let \(G\) be a finite group and let \(F(G)\) denote its Fitting subgroup. The main result of the paper is the following Theorem. \(C_G(F(G))=Z(F(G))\) if and only if there exists a nilpotent subgroup \(H\) of \(G\) such that \(C_G(H\cap H^g)=Z(H\cap H^g)\) for all \(g\in G\).
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Sylow subgroups
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maximal nilpotent subgroups
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centralizers
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Fitting subgroup
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