**ABELIAN OR 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

^{-1}à inverse of a
a.a

^{-1}= e = a^{-1}.a , ∀ a ∈ G**5)**

**Commutativity-**