> Given a homomorphism $f$, one must always salivate, like Pavlov's dog, by asking for its kernel and image; once these are known, there is a normal subgroup and $f$ can be converted into an isomorphism.

This colorful remark can be found in J. J. Rotman's *An introduction to the theory of groups* (last paragraph on page 35 of the 4th ed. of the book)... I recalled it recently as I was reading of the 172nd anniversary of [Ivan Pavlov][1]'s birth.


  [1]: https://en.wikipedia.org/wiki/Ivan_Pavlov