On some \(p\)-subgroups of automorphism group of a finite \(p\)-group. (Q935656)
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scientific article; zbMATH DE number 5310216
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On some \(p\)-subgroups of automorphism group of a finite \(p\)-group. |
scientific article; zbMATH DE number 5310216 |
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On some \(p\)-subgroups of automorphism group of a finite \(p\)-group. (English)
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12 August 2008
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Various subgroups of \(\Aut(G)\) are considered for a finite nonabelian \(p\)-group \(G\). These subgroups contain \(\text{Inn}(G)\) and are acting trivially on various characteristic subgroups of \(G\) and/or on various factor groups of \(G\). The main results give necessary and sufficient conditions for these subgroups of \(\Aut(G)\) to coincide with \(\text{Inn}(G)\), which is very useful for the detection of noninner automorphisms of \(p\)-power order.
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finite \(p\)-groups
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automorphism groups
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automorphisms of prime power order
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