On \(\pi\)-\(T^*\) groups (Q1592780)
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scientific article; zbMATH DE number 1556574
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On \(\pi\)-\(T^*\) groups |
scientific article; zbMATH DE number 1556574 |
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On \(\pi\)-\(T^*\) groups (English)
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21 January 2002
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Let \(G\) be a finite group and fix a set \(\pi\) of primes dividing the order of \(G\). The author calls \(G\) a \(\pi\)-\(T^*\) group if all subnormal \(\pi\)-subgroups of \(G\) are quasinormal in \(G\) (quasinormal: permutes with every Sylow subgroup of \(G\)). Two results are given, which characterize the situation where a solvable group \(G\) and all its subgroups are \(\pi\)-\(T^*\) groups.
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finite groups
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subnormal subgroups
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\(\pi\)-subgroups
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solvable groups
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quasinormal subgroups
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Sylow subgroups
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