(adsbygoogle = window.adsbygoogle || []).push({}); 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.

g^{n}[tex]\in[/tex] G = 1_{G}

and we know that [tex]\varphi[/tex] (g^{n})= 1_{G'}

But i dont really no what to do from here. It doesnt seem as if i am on the right track.

Any thoughts?

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# Homework Help: Groups whose orders have no common factors

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