Engel groups with an identity

2018/05/31 by Shumyatsky, Pavel, Tortora, Antonio, Tota, Maria
#20E26 #20F40 #20F45 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1805.12411

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.

Related

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• Profinite groups with an automorphism whose fixed points are right Engel