On \(c\)-normal subgroups of finite groups. (Q2714380)
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scientific article; zbMATH DE number 1604283
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On \(c\)-normal subgroups of finite groups. |
scientific article; zbMATH DE number 1604283 |
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22 June 2005
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\(c\)-normal subgroups
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maximal subgroups
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\(p\)-nilpotent groups
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On \(c\)-normal subgroups of finite groups. (English)
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A subgroup \(H\) of a finite group \(G\) is \(c\)-normal in \(G\) if \(G>N\) such that \(G=HN\) and \(H\cap N\) lies in the core of \(H\). The authors investigate the influence of \(c\)-normality of some subgroups of \(G\). For example, (Theorem 3.4): If \(p\) is the least prime factor of the order of \(G\) and all the maximal subgroups of a Sylow \(p\)-subgroup of \(G\) are \(c\)-normal in \(G\), then \(G\) is \(p\)-nilpotent.
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