Finite \(p\)-group with small Abelian subgroups. (Q355724)
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scientific article; zbMATH DE number 6191162
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finite \(p\)-group with small Abelian subgroups. |
scientific article; zbMATH DE number 6191162 |
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Finite \(p\)-group with small Abelian subgroups. (English)
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25 July 2013
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Summary: A finite \(p\)-group \(G\) is said to have the property \(P\), if, for any Abelian subgroup \(M\) of \(G\), there is \(|MZ(G)/Z(G)|\leq p\). We show that if \(G\) satisfies \(P\), then \(G\) has the following two types: (1) \(G\) is isoclinic to some stem groups of order \(p^5\), which form an isoclinic family. (2) \(G\) is isoclinic to a special \(p\)-group of exponent \(p\). Elementary structures of groups with \(P\) are determined.
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finite \(p\)-groups
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regular \(p\)-groups
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isoclinism families
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stem groups
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