Some new properties of non-abelian tensor analogues of ۲-auto Engel groups

In this paper, we study the concept of ۲_{\otimes}-auto Engel groups. Among other results, we prove that for any group G, if every element of G\otimes Aut(G) is ۲_{\otimes}-Engel group, then \left<(g\otimes\alpha),(g\otimes\alpha)^{g^{\prime}\otimes\alpha^{\prime}}\right> is a nilpotent subgroup of class at most ۲ in G\otimes Aut(G), for all g,g^{\prime} \in G and \alpha ,\alpha^{\prime}\in Aut(G).

Keywords:

Non-abelian tensor product , auto Engel element , autocommutator subgroup