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 R 2 (G) = fa 2 Gj[a; g] g = 1 ; 8g 2 Gg of right 2 -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] g = 1 , for all x; g; y 2 G. In particular p-groups satisfying the law [x; g; y] g = 1 have abelian tensor squares. Moreover, we can determine tensor squares of two-generator p-groups of class three satisfying the law [x; g; y] g = 1 .