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...