Group action

In mathematics Mathematics

Mathematics is the discipline that deals with concepts such as quantity [i], structure [i], space [i] a ... 

, a symmetry group Symmetry group

The symmetry [i] group of an object is the group [i] of all isometries [i] under which it is invariant [i] ... 

 describes all symmetries Symmetry

Symmetry is a characteristic feature of geometrical [i] shapes, system [i]s, equation [i]s, and ... 

 of objects. This is formalized by the notion of a group action: every element of the group "acts" like a bijective map on some set. In this case, the group is also called a permutation group  or transformation group .

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Encyclopedia

In mathematics Mathematics

Mathematics is the discipline that deals with concepts such as quantity [i], structure [i], space [i] a ... 

, a symmetry group Symmetry group

The symmetry [i] group of an object is the group [i] of all isometries [i] under which it is invariant [i] ... 

 describes all symmetries Symmetry

Symmetry is a characteristic feature of geometrical [i] shapes, system [i]s, equation [i]s, and ... 

 of objects. This is formalized by the notion of a group action: every element of the group "acts" like a bijective map on some set. In this case, the group is also called a permutation group or transformation group .

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