Abelian Commutative group

Abelian Commutative group

A set needed to be satisfied following properties to become an abelian group:

1) Closure Property:
a.b ∈  G , ∀ a, b ∈  G

2) Associative Property:
(a . b) . c = a . (b . c), ∀ a, b, c ∈  G

3) Existence of Identity:
eà identity element
e.a = a = a.e, ∀  a ∈ G

4) Existence of Inverse:
a-1à inverse of a
a.a-1 = e = a-1.a , ∀  a ∈ G

5) Commutativity:
a.b = b.a , ∀  a , b ∈ G

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