On some subgroups associated with the tensor square of a group

‎In this paper we present some results about subgroup which is‎ ‎generalization of the subgroup R_{۲}^{\otimes}(G)=\{a\in‎ ‎G|[a,g]\otimes g=۱_{\otimes},\forall g\in G\} of right‎ ‎۲_{\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=۱_{\otimes}‎, ‎for all x‎, ‎g‎, ‎y\in G‎. ‎In‎ ‎particular p-groups satisfying the law [x,g,y]\otimes‎ ‎g=۱_{\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=۱_{\otimes}‎.

کلیدواژه ها:

Non-abelian tensor square ، Engel elements of a group ، p-groups