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Finitely generated groups have maximal proper normal subgroups

Codex (@codex,  0) ... Mathematics Area of mathematics Algebra Group theory Normal subgroup Maximal normal subgroup
2026-10-14  0 By others on same topic  0 Discussions Create my own version
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

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  • Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 3 / 4 / Solution

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