A generalization of a theorem of Shidov. (Q2504971)
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scientific article
| Language | Label | Description | Also known as |
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| English | A generalization of a theorem of Shidov. |
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A generalization of a theorem of Shidov. (English)
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28 September 2006
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The authors, generalizing a result of \textit{L. I. Shidov} [Sib. Mat. Zh. 12, 682-683 (1971; Zbl 0219.20018)], determine formations \(\mathcal F\) of finite groups such that, for any insoluble group \(G\), the intersection \(\mathcal{F(G)}\) of the maximal subgroups of \(G\) which do not belong to \(\mathcal F\) coincides with the Frattini subgroup of \(G\).
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finite groups
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maximal subgroups
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saturated formations
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