Subgroups of system normalizers (Q1841845)
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scientific article; zbMATH DE number 1565879
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Subgroups of system normalizers |
scientific article; zbMATH DE number 1565879 |
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Subgroups of system normalizers (English)
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27 February 2002
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The major result of the present paper is Satz (3.4): Let \(G\) be a finite soluble group and \(U\) a subgroup of the system normaliser of \(G\). Then \(G\) has a pronormal nilpotent subgroup \(L\) such that the normaliser \(N\) of \(L\) in \(G\) operates transitively on the set of those conjugates of \(U\) which are contained in \(N\). The question is raised whether \(N\) is a Carter subgroup of \(G\) if \(U\) is a system normaliser of \(G\).
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finite soluble groups
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system normalisers
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pronormal nilpotent subgroups
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Carter subgroups
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0.7609570622444153
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0.759814977645874
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