Theorems · Inductive type · group theory
Group.FG
(G : Type u_3) → [Group G] → Prop
A group is finitely generated if it is finitely generated as a subgroup of itself.
- Defined in
- Mathlib.GroupTheory.Finiteness
- Cited by
- 40 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement · cited by 6,238
Cited by44
Results whose statement or proof uses this declaration.
- Group.rankstatement and proof · cited by 20
- CommGroup.freeRankstatement and proof · cited by 6
- Group.rank_specstatement and proof · cited by 5
- Group.rank_lestatement and proof · cited by 4
- Group.FG.outstatement and proof · cited by 4
- Group.fg_of_surjectivestatement and proof · cited by 3
- Group.rank_le_of_surjectivestatement and proof · cited by 3
- Subgroup.rank_congrstatement and proof · cited by 2
- Group.fg_defstatement and proof · cited by 2
- Group.fg_iff_monoid_fgstatement and proof · cited by 2
- Group.fg_iff_subgroup_fgstatement · cited by 2
- Group.rank_eq_zero_iffstatement and proof · cited by 2