1. The problem statement, all variables and given/known data Let G and G' be finite groups whose orders have no common factor. Prove that the homomorphism [tex]\varphi[/tex] G [tex]\rightarrow[/tex] G' is the trivial one [tex]\varphi[/tex] (x) =1 for all x. 3. The attempt at a solution My thoughts are that we need to use lagrange's thm. somehow. or maybe not. We have the order of G and G' such that. GCD( |G|, |G'|) =1. [tex]\varphi[/tex] G [tex]\rightarrow[/tex] G' Let |G| = n By legranges thm. gn [tex]\in[/tex] G = 1G and we know that [tex]\varphi[/tex] (gn)= 1G' But i dont really no what to do from here. It doesnt seem as if i am on the right track. Any thoughts?