Finite \(p\)-groups all of whose cyclic subgroups \(A,B\) with \(A\cap B\neq\{1\}\) generate an Abelian group. (Q375748)
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scientific article; zbMATH DE number 6221609
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finite \(p\)-groups all of whose cyclic subgroups \(A,B\) with \(A\cap B\neq\{1\}\) generate an Abelian group. |
scientific article; zbMATH DE number 6221609 |
Statements
Finite \(p\)-groups all of whose cyclic subgroups \(A,B\) with \(A\cap B\neq\{1\}\) generate an Abelian group. (English)
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31 October 2013
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In this deep paper the author classifies the \(p\)-groups with the title property. A number of results of Mann, Chillag-Mann, Hogan-Kappe and Laffey is used. As the preliminary results, the minimal nonabelian and metacyclic \(p\)-groups with the title property are classified. Even these results are non-trivial.
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finite \(p\)-groups
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minimal nonabelian \(p\)-groups
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metacyclic \(p\)-groups
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