On finite Alperin 2-groups with elementary Abelian second commutants. (Q1760517)
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scientific article; zbMATH DE number 6105693
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On finite Alperin 2-groups with elementary Abelian second commutants. |
scientific article; zbMATH DE number 6105693 |
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On finite Alperin 2-groups with elementary Abelian second commutants. (English)
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14 November 2012
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A \(p\)-group is said to be an Alperin \(p\)-group if all its two-generator subgroups have cyclic derived subgroups. The author presents the Alperin \(2\)-group \(G\), generated by \(n\geq 3\) involutions, the order of \(G\) is equal to \(2^{\frac12n(3n-1)}\) and its second derived subgroup is elementary Abelian of rank \(\frac12(n-1)(n-2)\). The proof is completely computational.
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finite 2-groups
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Alperin groups
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commutator subgroup
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two-generator subgroups
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presentations
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generators and relations
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