Three basic theorems, confusingly more about the behaviour of homomorphisms than that of isomorphisms (they show what certain objects generated using a homomorphism are isomorphic to). These are considerably more universal than would appear; natural generalisations hold outside group theory, e.g. in ring theory, linear algebra, and more exotic areas. In the language of category theory, they hold for Abelian categories, of which these are all examples.

Note the exceedingly original terminology:

One of the coolest things about the isomorphism theorems and something not everyone seems to remember is that they were first formulated (at least explicitly) by Emmy Noether. Indeed, some people refer to these as "Noether's isomorphism theorems". They are very characteristic of her work and her methods.

In the words of one of Noether's colleagues P. S. Alexandroff, in her approach to algebra she "taught us to think in simple, and thus general terms... homomorphic images, the group or ring with operators, the ideal... and not in complicated algebraic calculations," which is exactly what the isomorphism theorems are -- simpler terms. Next time you quotient an algebraic structure by the kernel of some homomorphism, remember Noether.

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