Abstract
A group G is said to be an n ⊗-Engel, if [y, n−1 x] ⊗ x = 1 for all x, y ∈ G, and we say a group G is tensor nilpotent of class at most n, if . In this article, we show that if G is a 3⊗-Engel group, then ⟨ x, x y ⟩ is tensor nilpotent of class at most 2, for all x, y ∈ G. We also prove that if G is a 4⊗-Engel group and G ⊗ G is torsion-free, then ⟨ x, x y ⟩ is tensor nilpotent of class at most 4, for all x, y ∈ G.
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