On locally graded groups with a word whose values are Engel. (Q2806133)
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scientific article; zbMATH DE number 6580778
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On locally graded groups with a word whose values are Engel. |
scientific article; zbMATH DE number 6580778 |
Statements
13 May 2016
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locally graded groups: multilinear commutators
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Engel elements
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outer commutator words
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verbal subgroup
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On locally graded groups with a word whose values are Engel. (English)
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Multilinear commutators (= outer commutator words) have the form of nested commutators without repetition of variables. R. Bastos and the authors of the article under review have considered the situation of locally graded groups in which the word \(w\) (a given multilinear commutator) has as values only \(n\)-Engel elements. They showed that the verbal subgroup \(w(G)\) is locally nilpotent. The authors generalize this result to the case that \(w\) is the \(n\)-th power of a multilinear commutator.
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