A generalization of the Hall-Witt identity (Q1678487)
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scientific article; zbMATH DE number 6808412
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A generalization of the Hall-Witt identity |
scientific article; zbMATH DE number 6808412 |
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A generalization of the Hall-Witt identity (English)
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17 November 2017
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The Hall-Witt formula \[ [[x_3,x_1^{-1}],x_2]^{x_1}[[x_1,x_2^{-1}],x_3]^{x_2}[[x_2,x_3^{-1}], x_1]^{x_3} = 1 \] is a kind of three-variable identity which is true in every group. In this paper, the Hall-Witt property of a word \(w\) is defined and it is shown how an infinite number of Hall-Witt-type identities in many variables can be generated by \(w\).
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commutator identity
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