Some new properties of non-abelian tensor analogues of 2-auto Engel groups

In this paper, we study the concept of 2⊗-auto Engel groups. Among other results, we prove that for any group G, if every element of G⊗Aut(G) is 2⊗-Engel group, then ⟨(g ⊗ α),(g ⊗ α) g′⊗α′⟩ is a nilpotent subgroup of class at most 2 in G ⊗ Aut(G), for all g, g′ ∈ G and α, α′ ∈ Aut(G).