On \(S\)-quasinormally embedded subgroups of finite groups (Q5954068)
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scientific article; zbMATH DE number 1698488
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On \(S\)-quasinormally embedded subgroups of finite groups |
scientific article; zbMATH DE number 1698488 |
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On \(S\)-quasinormally embedded subgroups of finite groups (English)
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5 March 2003
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This paper considers the consequences of a finite group \(G\) having special families of subgroups that are \(S\)-quasinormally embedded in \(G\). Sample result: Theorem 3.1. Let \(G\) be a finite group and let \(p\) be the smallest prime dividing \(|G|\). Then the following are equivalent: (a) \(G\) is \(p\)-nilpotent; (b) The maximal subgroups of the Sylow \(p\)-subgroups of \(G\) are \(S\)-quasinormally embedded in \(G\).
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\(S\)-quasinormally embedded subgroups
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nilpotent groups
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Sylow subgroups
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maximal subgroups
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