Power Groups and Order Relations

Abstract:

      Let G be a non-monoidal group, E be a normal subsemigroup of G such that E²=E and 1_G∈/ E. Then we can define a partial order in G by setting E as the positive cone, and G becomes a partially ordered group. Then we can study both the group G and power group Гon G with identity E by the order. The structure of G is clear if the order is maximal and the power group Г on G can be expanded to be of quasi-quotient type if G is lattice ordered.