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