Products of Sylow groups (Q1337751)
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scientific article; zbMATH DE number 687020
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Products of Sylow groups |
scientific article; zbMATH DE number 687020 |
Statements
Products of Sylow groups (English)
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13 November 1994
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The authors prove that a finite group \(G\) is solvable if and only if the product in any order of any representative set of Sylow subgroups of \(G\) equals \(G\), where a representative set of Sylow subgroups is one that contains exactly one Sylow \(p\)-subgroup for each prime \(p\) dividing the order of the group. That confirms a conjecture made (implicitly) by Philip Hall.
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finite solvable groups
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product of Sylow subgroups
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