Finite groups with given system of subgroups (Q2736159)

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scientific article; zbMATH DE number 1638289
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Finite groups with given system of subgroups
scientific article; zbMATH DE number 1638289

    Statements

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    29 August 2001
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    formations of finite groups
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    superradical formations
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    hereditary formations
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    \(\mathfrak F\)-subnormal subgroups
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    \(\mathfrak F\)-abnormal subgroups
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    Finite groups with given system of subgroups (English)
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    Let \(\mathfrak F\) be a formation of finite groups. \(\mathfrak F\) is called a superradical formation if it is an \(\mathfrak F\)-normal hereditary formation and \(G=AB\in{\mathfrak F}\), where \(A\) and \(B\) are \(\mathfrak F\)-subnormal \(\mathfrak F\)-subgroups of the group \(G\). A description of finite groups for which any proper subgroup is either \(\mathfrak F\)-subnormal or \(\mathfrak F\)-abnormal for an arbitrary solvable superradical formation \(\mathfrak F\) is obtained.
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