How can I show that the free group with 2 generators is not solvable? After that how can I show that the only free group that is solvable is the group with one generator?
ok, suppose you know the homomorphic image of a solvable group is solvable. suppose you find a group with 2 generators that ISN'T solvable.
isn't such a group a quotient group of the free group on two generators? and aren't quotient groups of a group just homomorphic images of that group
(the first isomorphism theorem)?