Group Action And Its Applications

ABSTRACT

 In mathematics, a symmetry groups describes all symmeiries of objects. This is formalized by the notion of a group action. A group G is said to act on a set x when there is a map 0 : C x X — X such that the foilowing conditiot bold for all elements x €X 0 (e, x) = X (where e is the identity elements of G) and øfg. 0(h,x) = 0(xh,x ) for all g, hCG. In this case, G is called a transformation group, x is called a O - set and 0 is called the group action. This group action can be applied in many branches of mathematics including algebra, topology, analysis as well as other braches of mathematics.