A characterization of permutation modules extending a theorem of Weiss (Q2006009)
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scientific article; zbMATH DE number 7258093
| Language | Label | Description | Also known as |
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| English | A characterization of permutation modules extending a theorem of Weiss |
scientific article; zbMATH DE number 7258093 |
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A characterization of permutation modules extending a theorem of Weiss (English)
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8 October 2020
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Summary: Let \(G\) be a finite \(p\)-group with normal subgroup \(N\). A celebrated theorem of A. Weiss gives a sufficient condition for a \(\mathbb{Z}_pG\)-lattice to be a permutation module, looking only at its restriction to \(N\) and its \(N\)-fixed points. In case \(N\) has order \(p\), we extend the condition of Weiss to a characterization.
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permutation modules
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finite \(p\)-groups
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