Group
An algebra structure of set G & a binary operation* defined in G( G,*) is called a group if * satisfies the following postulates:
1 Associativity
(a*b)*c=a*(b*c). For every a,b,c€G
2 Existence of Identity
e*a=a*e=a. a€ G
3 Existence of inverse
a*b=b*a=e