Prove that there is only one possible multiplication table for
G if G has exactly 1, 2, or 3 elements. Analyze the possible
multiplication tables for groups with exactly 4 elements, and show
that there are two distinct tables, up to reordering the elements
of G. Use these tables to prove that all groups with < 4
elements are commutative.
(You are welcome to analyze groups
with 5 elements using the same technique, but you will soon know
enough about...