ON SOME SUBGROUPS ASSOCIATED WITH THE TENSOR SQUARE OF A GROUP

Abstract. in this paper we present some results about subgroup which is generalization of the sub-group r2 (g) = fa 2 gj[a; g] g = 1; 8g 2 gg of right 2-engel elements of a given group g. ifp is an odd prime, then with the help of these results, we obtain some results about tensor squaresof p-groups satisfying the law [x; g; y] g = 1, for all x; g; y 2 g. in particular p-groups satisfyingthe law [x; g; y] g = 1 have abelian tensor squares. moreover, we can determine tensor squares oftwo-generator p-groups of class three satisfying the law [x; g; y] g = 1.