Abstract
Let m, n be positive integers, v amultilinear commutatorword and w = v m. We prove that if G is an orderable group in which all w-values are n-Engel, then the verbal subgroup v(G) is locally nilpotent. We also show that in the particular case where v = x the group G is nilpotent (rather than merely locally nilpotent).
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This work was carried out during the first author’s visit to the University of Salerno. He would like to thank the Department of Mathematics for hospitality and GNSAGA and CNPq–Brazil for support.
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Shumyatsky, P., Tortora, A. & Tota, M. An Engel condition for orderable groups. Bull Braz Math Soc, New Series 46, 461–468 (2015). https://doi.org/10.1007/s00574-015-0100-3
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DOI: https://doi.org/10.1007/s00574-015-0100-3