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arXiv · 1805.12411

Engel groups with an identity

Pavel Shumyatsky·Antonio Tortora·Maria Tota
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Abstract

We give an affrmative answer to the question whether a residually finite Engel group satisfying an identity is locally nilpotent. More generally, for a residually finite group G with an identity, we prove that the set of right Engel elements of G is contained in the Hirsch-Plotkin radical of G. Given an arbitrary word w, we also show that the class of all groups G in which the w-values are right n-Engel and w(G) is locally nilpotent is a variety.

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Pavel Shumyatsky, Antonio Tortora, Maria Tota. 2018-05-31. Engel groups with an identity. https://arxiv.org/abs/1805.12411

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