Homework Statement
Let G be a nonempty finite set with an associative binary operation such that:
for all a,b,c in G
ab = ac => b = c
ba = ca => b = c
(left and right cancellation)
Prove that G is a group.
2. The attempt at a solution
Let a \in G, the set <a> = {a^k : k \in N} is a finite...