Sylow permutable subnormal subgroups of finite groups. II (Q2777723)
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scientific article; zbMATH DE number 1717652
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sylow permutable subnormal subgroups of finite groups. II |
scientific article; zbMATH DE number 1717652 |
Statements
5 May 2002
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permutability conditions
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Hall subgroups
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\(\text{PST}_p\)-groups
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soluble groups
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subnormal \(p'\)-perfect subgroups
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0.97706467
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0.94607097
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0.9418484
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0.92990553
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0.92548263
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0.9244865
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Sylow permutable subnormal subgroups of finite groups. II (English)
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\(\text{PST}_p\)-groups are soluble groups \(G\) with the property that subnormal \(p'\)-perfect subgroups are permutable with all \(p'\)-Hall subgroups of \(G\). This is a localization of the property PST; PST-groups are \(\text{PST}_p\)-groups for all primes \(p\). -- The authors establish two criteria for the group to be a \(\text{PST}_p\)-group, one via the normal structure (Theorem A), the other via the embedding of \(p'\)-perfect subnormal subgroups (Theorem B).
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