Explore BrainMass
Share

# Proof regarding direct sum of 2 copies of (Q,+)

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Use the fact that any finitely generated subgroup of (Q,+), (the rationals under addition), is cyclic to show that (Q,+)+(Q,+), (the direct sum of two copies of (Q,+)), is not isomorphic to (Q,+). The first part of this was showing that any finitely generated subgroup of (Q,+) is cyclic and I understand that part and really had little difficulty with it, but this second part is proving far more difficult. Any help would be greatly appreciated.

https://brainmass.com/math/discrete-math/proof-regarding-direct-sum-copies-223661

#### Solution Preview

(In what follows, the group operation is addition throughout)

Consider the subgroup of generated by the elements and (this is just )
The cyclic subgroup generated ...

#### Solution Summary

This solution is comprised of a detailed explanation to proof regarding direct sum of 2 copies of (Q,+).

\$2.19