The Structures and Constructions of Power Group

With the applications of topological upgrading [1], some problems of upgrading mathematical structure to its power set have caused wide concerns. This paper studies the upgrading from group structure to its power set and gives the definition, examples and ways of construction of power groups, then shows the relationship between power groups and common groups and characterized power groups by common groups, and obtains a series of constructive conclusions and achieves many breakthroughs of upgrading a group to its power set.