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arXiv · 2002.06136

On residually finite groups satisfying an Engel type identity

Danilo Silveira
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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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Danilo Silveira. 2020-02-14. On residually finite groups satisfying an Engel type identity. https://doi.org/10.1007/s00605-020-01390-y

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