Theorems · Definition · group theory
Submonoid.FG
{M : Type u_1} → [inst : Monoid M] → Submonoid M → PropA submonoid of M is finitely generated if it is the closure of a finite subset of M.
- Defined in
- Mathlib.GroupTheory.Finiteness
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
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
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement and proof · cited by 3,086
- Submonoid.closureproof · cited by 167
Cited by26
Results whose statement or proof uses this declaration.
- Monoid.FG.fg_topstatement · cited by 7
- Subgroup.fg_iff_submonoid_fgstatement and proof · cited by 5
- Submonoid.fg_iffstatement and proof · cited by 4
- Submonoid.fg_iff_add_fgstatement and proof · cited by 3
- Submonoid.fg_of_divisivestatement · cited by 2
- Monoid.fg_defstatement and proof · cited by 2
- Monoid.fg_iff_submonoid_fgstatement and proof · cited by 2
- AddSubmonoid.fg_iff_mul_fgstatement and proof · cited by 2
- Submonoid.FG.biSupstatement and proof · cited by 1
- Submonoid.FG.biSup_finsetstatement and proof · cited by 1
- Submonoid.FG.botstatement · cited by 1
- Submonoid.FG.exists_minimal_closure_eqstatement and proof · cited by 1