Triple factorizations and supersolubility of finite groups. (Q2806117)
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scientific article; zbMATH DE number 6580763
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Triple factorizations and supersolubility of finite groups. |
scientific article; zbMATH DE number 6580763 |
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13 May 2016
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finite factorized groups
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supersoluble groups
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triple factorizations
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supersolubility
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groups of minimal order
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Triple factorizations and supersolubility of finite groups. (English)
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Finite groups \(G\) are studied that have a triple factorization \(G=HK=HL=KL\) with subgroups \(H\), \(K\) and \(L\). If \(H\), \(K\) and \(L\) are nilpotent, then \(G\) is nilpotent by a classical result of O. Kegel. On the other hand, there exist non-supersoluble groups that have a triple factorization by supersoluble subgroups even in the case when the three subgroups have pairwise relatively prime indices in the group. The authors analyze the structure of such groups with minimal order and give a method to construct such a minimal configuration. Some known results are derived as consequences.
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