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-

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