When you teach algebra to students, it's often easy to find cute/direct applications of "big" theorems to motivate how useful these results can be.

For example, group actions, Sylow theorems, or the first isomorphism theorems have nice applications and can provide non trivial results in few lines.

However, I'm struggling to find such applications concerning the Snake Lemma outside homological algebra (so the five/nine lemma is not a good example).

Precisely, I would like to know applications of the Snake Lemma, even direct and/or not very sophisticated, but which would have been difficult or lengthy to prove without it.

I found such an example here, which is rather sophisticated: Is an abelian group characterized by its localizations?

Maybe you will have other examples , even shorter or simpler?

Thanks for your help !


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