A non-abelian free pro-\(p\) group is not linear over a local field (Q1283280)
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scientific article; zbMATH DE number 1275267
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A non-abelian free pro-\(p\) group is not linear over a local field |
scientific article; zbMATH DE number 1275267 |
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A non-abelian free pro-\(p\) group is not linear over a local field (English)
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25 August 1999
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Pink's recent characterization of compact subgroups of \(\text{GL}_n(F)\), where \(F\) is a non-archimedian local field, is applied to prove that a free non-abelian pro-\(p\) group can not be linear over \(F\). This establishes a conjecture of Lubotzky and Shalev. Using a theorem of Zelmanov the authors deduce some group theoretic properties of linear pro-\(p\) groups over local fields.
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free pro-\(p\) groups
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linear pro-\(p\) groups over local fields
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