Finite \(p\)-groups all of whose maximal Abelian subgroups are soft. (Q625924)
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scientific article; zbMATH DE number 5857734
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finite \(p\)-groups all of whose maximal Abelian subgroups are soft. |
scientific article; zbMATH DE number 5857734 |
Statements
Finite \(p\)-groups all of whose maximal Abelian subgroups are soft. (English)
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25 February 2011
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It is shown that the following conditions are equivalent for a finite nonabelian \(p\)-group \(G\): 1) The automizers of all Abelian subgroups of \(G\) have maximum order \(p\). 2) Every maximal Abelian subgroup of \(G\) is soft. 3) \(G\) has an Abelian maximal subgroup and \(G/Z(G)\) is of maximal class.
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finite \(p\)-groups
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soft subgroups
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\(p\)-groups of maximal class
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automizers
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maximal Abelian subgroups
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