Can I get help on the following problem:
Is the additive group of rationals isomorphic to the multiplicative group of non-zero rationals.
There is another way to see the non-isomorphism. In there exists an element, different from the identity, which when multiplied on itself produces the identity. This is since . However, in under addition you cannot find an element which when added to itself will produce the identity other than the identity. Thus, the two cannot be isomorphic.