Homomorphism of Groups with Examples

In this class, We discuss the Homomorphism of Groups with Examples.

The reader should have prior knowledge of the group. Click Here.

Homomorphism:

Let [G *] and [H Δ] be two groups.

A mapping F: G -> H is said to be homomorphism if F(a * b) = F(a) Δ F(b).

Example:

G: [Z +]

H: [{0, 1, 2}, +mod3]

f: G -> H f(x) = x%3.

f(a + b) = f(a) +mod3 f(b)

(a + b)%3 = (a%3 + b%3)%3

(5 + 10)%3 = (5%3 + 10%3)%3

0 = 0