Theorems · Definition · group theory
Subgroup.FG
{G : Type u_3} → [inst : Group G] → Subgroup G → PropA subgroup of G is finitely generated if it is the closure of a finite subset of G.
- Defined in
- Mathlib.GroupTheory.Finiteness
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Subgroup.closureproof · cited by 196
Cited by20
Results whose statement or proof uses this declaration.
- Subgroup.fg_iff_submonoid_fgstatement and proof · cited by 5
- Group.FG.outstatement · cited by 4
- Group.fg_defstatement and proof · cited by 2
- Group.fg_iff_subgroup_fgstatement · cited by 2
- Subgroup.fg_iffstatement and proof · cited by 2
- Group.fg_iff'proof · cited by 1
- Subgroup.fg_iff_add_fgstatement · cited by 1
- AddSubgroup.fg_iff_mul_fgstatement and proof · cited by 1
- Subgroup.FG.biSupstatement and proof · cited by 1
- Subgroup.FG.biSup_finsetstatement and proof · cited by 1
- Subgroup.FG.botstatement · cited by 1
- Subgroup.FG.finset_supstatement and proof · cited by 1