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arXiv · 1208.5623

On groups admitting a word whose values are Engel

Raimundo Bastos·Pavel Shumyatsky·Antonio Tortora·Maria 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 a residually finite group in which all w-values are n-Engel, then the verbal subgroup w(G) is locally nilpotent. We also examine the question whether this is true in the case where G is locally graded rather than residually finite. We answer the question affirmatively in the case where m = 1. Moreover, we show that if u is a non-commutator word and G is a locally graded group in which all u-values are n-Engel, then the verbal subgroup u(G) is locally nilpotent.

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Raimundo Bastos, Pavel Shumyatsky, Antonio Tortora, Maria Tota. 2012-08-28. On groups admitting a word whose values are Engel. https://doi.org/10.1142/s0218196712500798

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