Finitely generated groups have maximal proper normal subgroups
= Finitely generated groups have maximal proper normal subgroups
Above any proper <normal subgroup> of a finitely generated group, a chain of proper <normal subgroups> has proper union. Otherwise that union would contain the finite <generating set>, all of which would already lie in one member of the chain. The <Zorn lemma> therefore provides a maximal proper <normal subgroup> containing the given one.
// Target: algebra.bigb