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arXiv · 1402.5247

An Engel condition for orderable groups

P. Shumyatsky·A. Tortora·M. Tota
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Abstract

Let m,n be positive integers, v a multilinear commutator word 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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P. Shumyatsky, A. Tortora, M. Tota. 2014-02-21. An Engel condition for orderable groups. https://arxiv.org/abs/1402.5247

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