Theorems · Theorem · group theory
Group.fg_iff_nonempty_finite_generators
∀ {G : Type u_1} [inst : Group G], Group.FG G ↔ ∃ n, Nonempty (Group.Generators G (Fin n))A group is finitely generated if and only if it admits a finite generating family.
- Defined in
- Mathlib.GroupTheory.Generators
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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Cites15
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