Nielsen generating sets and quasiconvexity of subgroups (Q1924670)
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scientific article; zbMATH DE number 937163
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nielsen generating sets and quasiconvexity of subgroups |
scientific article; zbMATH DE number 937163 |
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Nielsen generating sets and quasiconvexity of subgroups (English)
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27 May 1997
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For a finite set \(S\) of generators of a subgroup \(H<G\) a Nielsen property is defined and a modification of it, a weak Nielsen property. In the case of a free group \(G\) the first coincides with the usual Nielsen property. The authoress proves a certain equivalence between the weak Nielsen property and the quasi-convexity of \(H\) in \(G\). Another result states that a subgroup of a negatively curved group retains this property, if it has a weakly Nielsen generating set \(S\).
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Cayley graphs
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weak Nielsen property
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quasi-convexity
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negatively curved groups
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weakly Nielsen generating sets
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