GROUPS

Definition 1 (Group)

A group is a binary operation structure (G,*) is a nonempty set and * is a binary operation on G such that the following axioms are satisfied.

G1 : For all a, b, c in G,

(a*b)*c = a*(b*c)

Associativity of *

G2 : There is an element e in G such that for all x in G,

e*x = x*e = x

Identity of *

G3 : Corresponding to each a in G, there ia an element a' in G such that

a*a' = a'*a = e

Inverse a' of a

Note : If any of these axioms is not satisfied, then a binary structure is not a group.