Maximal Frattini \(p\)-modules of minimal nonsolvable groups, having cyclic Sylow \(p\)-subgroups (Q1076134)
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scientific article; zbMATH DE number 3953038
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Maximal Frattini \(p\)-modules of minimal nonsolvable groups, having cyclic Sylow \(p\)-subgroups |
scientific article; zbMATH DE number 3953038 |
Statements
Maximal Frattini \(p\)-modules of minimal nonsolvable groups, having cyclic Sylow \(p\)-subgroups (English)
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1985
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Let \(H\) be a finite group with the Frattini subgroup \(\Phi(H)\) and let \(G=H/\Phi(H)\). Suppose \(\Phi(H)\) is an elementary abelian \(p\)-subgroup for a prime \(p\). The author describes the structure of \(\Phi(H)\) as a \(G\)-module for the cases \(G=\mathrm{PSL}(2,q)\) or \(\mathrm{Sz}(2^ m)\) and a Sylow \(p\)-subgroup of \(G\) is cyclic.
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Frattini subgroup
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elementary abelian p-subgroup
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G-module
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