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 w...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.展开更多
文摘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.
