ON VARIETAL CAPABILITY OF INFINITE DIRECT PRODUCTS OF GROUPS

Abstract. Recently, the authors gave some conditions under which a direct product of finitely many groups is V-capable if and only if each of its factors is V-capable for some varieties V. In this paper, we extend this fact to any infinite direct product of groups. Moreover, we conclude some results for V-capability of direct products of infinitely many groups in varieties of abelian, nilpotent and polynilpotent groups.