Invariant generation (Q750609)
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scientific article; zbMATH DE number 4175234
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Invariant generation |
scientific article; zbMATH DE number 4175234 |
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Invariant generation (English)
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1988
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Definition. A (profinite) group G is invariantly generated by its (closed) subgroups \(G_ 0,...,G_ n\) if, for any \(g_ 0,...,g_ n\in G\), one has \(G=<G_ 0^{g_ 0},...,G_ n^{g_ n}>\). Main result: Let \(G_ 1\) and \(G_ 2\) be nontrivial profinite groups. Then their free product is not invariantly generated by \(G_ 1\) and \(G_ 2\).
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invariantly generated
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profinite groups
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free product
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