Normal subgroups are important because they (and only they) can be used to construct quotient groups of the given group. Furthermore, the normal subgroups of are precisely the kernels of group homomorphisms with domain , which means that they can be used to internally classify those homomorphisms.
Normal subgroups are important because they (and only they) can be used to construct quotient groups of the given group Furthermore, the normal .subgroups of are precisely the kernels of group homomorphisms with domain , which means that they can be used to internally classify those homomorphisms.