A note on kernels and vertices of simple modules (Q1346120)
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scientific article; zbMATH DE number 735331
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on kernels and vertices of simple modules |
scientific article; zbMATH DE number 735331 |
Statements
A note on kernels and vertices of simple modules (English)
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30 October 1995
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Let \(FG\) be the group algebra of a finite group over an algebraically closed field \(F\) of characteristic \(p>0\). It is shown that if the kernel of any simple \(FG\)-module \(S\) contains the vertex of \(S\) then \(G\) is \(p\)- solvable and the \(p\)-length of \(G/O_ p(G)\) is at most one or two according as \(p\neq 2\) or \(p=2\).
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simple modules
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\(p\)-solvable groups
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group algebras
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finite groups
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kernel
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vertex
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\(p\)-length
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0.8952620029449463
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0.8138511776924133
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0.8005434274673462
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0.7930479049682617
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0.7777870893478394
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