Automorphism groups of semidirect products. (Q998812)
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scientific article; zbMATH DE number 5500569
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Automorphism groups of semidirect products. |
scientific article; zbMATH DE number 5500569 |
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Automorphism groups of semidirect products. (English)
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29 January 2009
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Let \(G=K\cdot H\) be a semidirect product with kernel \(H\). Then \(\Aut(G)=C_{\Aut(G)}(H)C_{\Aut(G)}(K)\) if and only if \(K^\theta\cap H=\{1\}\) and \([K,\theta]\leq C_G(H)\) for all \(\theta\in\Aut(G)\). This result is applied to the study of the automorphism group of a split metacyclic \(p\)-group for \(p>2\).
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automorphism groups
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semidirect products
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metacyclic \(p\)-groups
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