Finite groups in which pronormality and \(\mathfrak F\)-pronormality coincide. (Q254324)
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scientific article; zbMATH DE number 6551809
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finite groups in which pronormality and \(\mathfrak F\)-pronormality coincide. |
scientific article; zbMATH DE number 6551809 |
Statements
Finite groups in which pronormality and \(\mathfrak F\)-pronormality coincide. (English)
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8 March 2016
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For a formation \(\mathfrak F\) of groups, \(\mathfrak F\)-pronormal subgroups \(U\subseteq G\) satisfy \(U^g=U^x\) with \(x\in\langle U,U^g\rangle^{\mathfrak F}\) for all \(g\in G\). (For \(\mathfrak N\) the formation of nilpotent groups, \(\mathfrak N\)-pronormal subgroups are just pronormal subgroups.) The authors describe formations of solvable groups with the property of the title with a special look at supersolvable groups.
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finite groups
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solvable groups
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supersolvable groups
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formations
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generalized pronormality
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pronormal subgroups
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