Group,Subgroup


G is a group under operation *.
  1. Associativity

  2. Existence of the unit element

  3. Existence of the inverse element


    Remark: expressed as .

Examples
Additive group
Multiplicative group
Group of motions
Symmetric group
Permutation group

Commutative group (Abelian group)


is a subgroup of .
  3. If then .
  4. If then .
The number of elements of a finite group G is called Order.


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