General
To generalise this to universal algebra, normal subgroups need to be replaced by congruences.
A congruence on an algebra is an equivalence relation which is a subalgebra of endowed with the component-wise operation structure. One can make the set of equivalence classes into an algebra of the same type by defining the operations via representatives; this will be well-defined since is a subalgebra of .
Read more about this topic: Isomorphism Theorem
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