Topological Loops with Decomposable Solvable Multiplication Groups

Abstract In this paper we deal with the class $$\mathcal {C}$$ C of decomposable solvable Lie groups having dimension six. We determine those in and their subgroups which are multiplication Mult ( L ) inner mapping Inn for three-dimensional connected simply topological loops . This result completes classification at most 6-dimensional Moreover, obtain that every 3-dimensional proper loop a group six as its is centrally nilpotent two.