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 infi nite direct product of groups. Moreover, we conclude some results for V-capability of direct products of infi nitely many groups in varieties of abelian, nilpotent and polynilpotent group.

Keywords

• Capable group
• Direct product
• Variety of groups
• V−capable group
• direct limit