[SOLVED] isomorphisms of groups

• September 24th 2007, 02:56 PM
danielap
[SOLVED] isomorphisms of groups
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.
• September 24th 2007, 06:29 PM
ThePerfectHacker
Quote:

Originally Posted by danielap
1). Are (Z, +) and (Q,+) isomorphic?

One iis cyclic and the other is not.

Quote:

2). Are Q, +) and (Q*, *) isomorphic?
Q* = nonzero rationals[/I]
No. This

Quote:

[I]3). Any finitely generated subgroup of (Q, +, 0) is cyclic.
Is $S = \{ 1, 1/2\}$ cyclic when generated?