Bounded Engel elements in residually finite groups

  • Raimundo Bastos
  • Danilo Silveira


Let q be a prime. Let G be a residually finite group satisfying an identity. Suppose that for every \(x \in G\) there exists a q-power \(m=m(x)\) such that the element \(x^m\) is a bounded Engel element. We prove that G is locally virtually nilpotent. Further, let dn be positive integers and w a non-commutator word. Assume that G is a d-generator residually finite group in which all w-values are n-Engel. We show that the verbal subgroup w(G) has \(\{d,n,w\}\)-bounded nilpotency class.


Engel elements Residually finite groups Verbal subgroups Non-commutator words 

Mathematics Subject Classification

20F45 20E26 



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Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade de BrasíliaBrasíliaBrazil
  2. 2.Departamento de MatemáticaUniversidade Federal de GoiásCatalãoBrazil

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