Finite \(p\)-groups all of whose non-normal Abelian subgroups are cyclic. (Q2847699)
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scientific article; zbMATH DE number 6207510
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finite \(p\)-groups all of whose non-normal Abelian subgroups are cyclic. |
scientific article; zbMATH DE number 6207510 |
Statements
11 September 2013
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finite \(p\)-groups
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non-normal Abelian subgroups
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cyclic subgroups
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minimal non-Abelian subgroups
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Finite \(p\)-groups all of whose non-normal Abelian subgroups are cyclic. (English)
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Let \(p\) be a prime. D. Passman has classified the \(p\)-groups, except the \(2\)-groups of order \(\leq 128\), all of whose non-normal subgroups are cyclic. This classification was finished in \S16 of the book by the reviewer and \textit{Z. Janko} [Groups of prime power order. Vol. 2. Berlin: Walter de Gruyter (2008; Zbl 1168.20002)]. In this paper the \(p\)-groups all of whose non-normal Abelian subgroups are cyclic, are classified thus supplementing the above stated result.
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