Please, is it possible for somebody to help me with this:

1). Are (Z, +) and (Q,+) isomorphic?

2). Are Q, +) and (Q*, *) isomorphic?

Q* = nonzero rationals

3). Any finitely generated subgroup of (Q, +, 0) is cyclic.

How do we do such kind of exercices? Do I need to find a counterexample?

Those are problems from Nathan Jacobson - Basic Algebra Vol. I.

There are somewhere on the web some old homeworks from this book?

I don't know how to post a message for everybody to see it...

Thank you.

Dana.