The free group on 3 generators is isomorphic to a subgroup of the free group on 2 generators.

Question

Possible Duplicate:
Is there a free subgroup of rank 3 in $SO_3$?

How is this possible?

Here are some facts:

1. $F_2 \subset F_3$

2. $F_2 \not\cong F_3$

Fact 2 implies that $F_3$ is isomorphic to a proper subgroup of $F_2$, i.e. one in which there are exist some relations between the generators of $F_2$.

But I'm really struggling to come up with anything else.