Finite nonabelian \(p\)-groups having exactly one maximal subgroup with a noncyclic center. (Q633169)
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scientific article; zbMATH DE number 5872599
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finite nonabelian \(p\)-groups having exactly one maximal subgroup with a noncyclic center. |
scientific article; zbMATH DE number 5872599 |
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Finite nonabelian \(p\)-groups having exactly one maximal subgroup with a noncyclic center. (English)
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31 March 2011
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The paper answers Problem 2036 of the book by \textit{Y. Berkovich} and \textit{Z. Janko}, [Groups of prime power order. Vol. 3. Berlin: Walter de Gruyter (2011; Zbl 1229.20001)], namely, to classify finite nonabelian \(p\)-groups with exactly one maximal subgroup having noncyclic center as those with cyclic center and only one normal Abelian subgroup of type \((p,p)\). Furthermore, the author describes finite nonabelian \(p\)-groups with all nonabelian maximal subgroups having cyclic center.
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finite \(p\)-groups
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center
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nonabelian maximal subgroups
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