n-BELL PROPERTY ON INFINITE SUBSETS OF GROUPS

Let n > 1 be an integer and Bn be the variety n-Bell groups, defined by the law [xn; y][x; yn]¡1 = 1. Let B¤n be the class of groups in which for any infinite subset X and Y , there exist x 2 X and y 2 Y such that [xn; y][x; yn]¡1 = 1. In this paper we prove that B¤n = Bn S F, where F is the class of finite groups