Abstract
The following theorem is proved. For any positive integers n and k there exists a number s = s(n, k) depending only on n and k such that the class of all groups G satisfying the identity \({\left(\left[x_1, {}_ky_1\right] \cdots \left[x_s, {}_ky_s\right]\right)^n \equiv 1}\) and having the verbal subgroup corresponding to the kth Engel word locally finite is a variety.
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Communicated by D. Segal.
The Pavel Shumyatsky was supported by CNPq and FINATEC and Jhone Caldeira Silva was supported by CNPq and Capes.
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Shumyatsky, P., Silva, J.C. Engel words and the Restricted Burnside Problem. Monatsh Math 159, 397–405 (2010). https://doi.org/10.1007/s00605-008-0050-6
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DOI: https://doi.org/10.1007/s00605-008-0050-6