Prove that every finitely generated subgroup of a totally ordered group can be totally ordered. A group can be totally ordered if there is a total order $\leq $ on that group.
Is the proof of this trivial? What facts should I use to prove this? I only have second year abstract algebra knowledge and never learned about ordered groups or finitely generated groups before but I know their definitions. I am just unsure whether there are theorems, properties, or lemmas for such groups to help prove this fact.
Should I use Zorn's lemma?