in this article we introduce the notion of n-capable groups. it is shown that every group g admits a uniquely determined subgroup (〖z^n)〗^* (g) which is a characteristic subgroup and lies in the n-centre subgroup of the group g. this is the smallest subgroup of g whose factor group is n-capable. moreover, some properties of n-central extension will be studied.

Abstract Background Artificial agriculture is promoted as an economically viable technology for developing plants under controlled conditions whereby light, water, and fertilizer intake are regulated in a manner to produce maximum productivity with minimal resources. light has been used high-quality vegetables because it can regulate plant growth phytochemical production through intensity, phot...