The classification of the finite groups whose subgroups of equal order are conjugate. (Q441369)
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scientific article; zbMATH DE number 6070495
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The classification of the finite groups whose subgroups of equal order are conjugate. |
scientific article; zbMATH DE number 6070495 |
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The classification of the finite groups whose subgroups of equal order are conjugate. (English)
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23 August 2012
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A finite group \(G\) is a \(B\)-group if the subgroups of \(G\) of equal order are conjugate. The author continues and completes his investigation into \(B\)-groups, giving necessary and sufficient conditions for a finite group to be a \(B\)-group. These conditions come in various guises, dependent on whether \(G\) is soluble, whether a Sylow 2-subgroup is Abelian, normal, etc. The proofs are detailed and technical.
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finite groups
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conjugate subgroups
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Hall subgroups
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Sylow subgroups
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equal order subgroups
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\(B\)-groups
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