Isomorphism

An isomorphism is a morphism that is bijective.

If we say the morphism from Group A to Group B is bijective, then we have a morphism from Group B to Group A.

A={1,2,3} and B={2,4,6}

• 1–>2
• 2–>4
• 3–>6

We can go from B to A by reversing each of the three arrows.

Now compare this to

A={1,2,3} and B={2,4,6,8,10}

where when we try to go from B to A we have a “crash” when 8 and 10 try to find something in A for mapping.

Appendix A

Congruence and Similarity are examples of Isomorphism.

Appendix B

Let f be a bijective function from Group G1 to Group G2.

Let a,b be any two elements in G1.

If f(a*b) = f(a)*f(b) then f is an Isomorphism from G1 to G2.