University of Isfahan International Journal of Group Theory 2251-7650 2 2 2013 06 01 On some subgroups associated with the tensor square of a group 25 33 1897 10.22108/ijgt.2013.1897 EN Mohammad Mehdi Nasrabadi Department of Maths,birjand university Ali Gholamian Department of math, birjand university Mohammad Javad Sadeghifard Islamic Azad University, Neyshabur branch Journal Article 2012 05 07 ‎In this paper we present some results about subgroup which is‎ ‎generalization of the subgroup $R_{2}^{\otimes}(G)=\{a\in‎ ‎G|[a,g]\otimes g=1_{\otimes},\forall g\in G\}$ of right‎ ‎$2_{\otimes}$-Engel elements of a given group $G$‎. ‎If $p$ is an‎ ‎odd prime‎, ‎then with the help of these results‎, ‎we obtain some‎ ‎results about tensor squares of p-groups satisfying the law‎ ‎$[x,g,y]\otimes g=1_{\otimes}$‎, ‎for all $x‎, ‎g‎, ‎y\in G$‎. ‎In‎ ‎particular p-groups satisfying the law $[x,g,y]\otimes‎ ‎g=1_{\otimes}$ have abelian tensor squares‎. ‎Moreover‎, ‎we can‎ ‎determine tensor squares of two-generator p-groups of class three‎ ‎satisfying the law $[x,g,y]\otimes g=1_{\otimes}$‎. https://ijgt.ui.ac.ir/article_1897_1f5905dcbdef0eadf29d39b9305e74be.pdf