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

Document Type : Research Articles

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Department of Mathematics, Esfarayen University of Technology, Esfarayen, Iran

Abstract

In this paper, we study the concept of $2_{\otimes}$-auto Engel groups. Among other results, we prove that for any group $G$, if every element of $G\otimes Aut(G)$ is $2_{\otimes}$-Engel group, then $\left<(g\otimes\alpha),(g\otimes\alpha)^{g^{\prime}\otimes\alpha^{\prime}}\right>$ is a nilpotent subgroup of class at most $2$ in $G\otimes Aut(G)$, for all $g,g^{\prime} \in G$ and $\alpha ,\alpha^{\prime}\in Aut(G)$.

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