摘要
Let G be a non-monoidal group, E be a normal subsemigroup of G such that E 2=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 Г on 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.
设Ｇ为非ｍｏｎｏｉｄａｌ群，Ｅ是它的正规子集，满足Ｅ２＝Ｅ并且１Ｇ∈／Ｅ．利用Ｅ作为正锥，可以在Ｇ上定义一个偏序，并且Ｇ成为一个偏序群．这样就可以利用这个序关系同时研究群Ｇ以及Ｇ上的以Ｅ为单位元的幂群．当Ｅ是极大子半群时，得到Ｇ的一个结构定理；在Ｇ是格序群的条件下，Ｇ上的幂群Γ可以膨胀为一个拟商群．
