Abstract
Let n, q be positive integers. We show that if G is a finitely generated residually finite group satisfying the identity \([x,_ny^q]\equiv 1\), then there exists a function f(n) such that G has a nilpotent subgroup of finite index of class at most f(n). We also extend this result to locally graded groups.
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This work was supported by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) - Brazil.
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Communicated by John S. Wilson.
Dedicated to Pavel Shumyatsky on the occasion of his 60th birthday.
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Silveira, D. On residually finite groups satisfying an Engel type identity. Monatsh Math 193, 171–176 (2020). https://doi.org/10.1007/s00605-020-01390-y
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DOI: https://doi.org/10.1007/s00605-020-01390-y