Theorems · Theorem · group theory
Subgroup.closure_toSubmonoid_of_isOfFinOrder
∀ {G : Type u_1} [inst : Group G] {s : Set G},
(∀ x ∈ s, IsOfFinOrder x) → (Subgroup.closure s).toSubmonoid = Submonoid.closure sSee Subgroup.closure_toSubmonoid_of_finite for a version for finite groups.
- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 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.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Groupstatement and proof · cited by 6,238
- Submonoidstatement and proof · cited by 3,086
- le_antisymmproof · cited by 2,068
- Subgroup.closurestatement · cited by 196
- Submonoid.closurestatement and proof · cited by 167
- Subgroup.toSubmonoidstatement · cited by 114
- IsOfFinOrderstatement and proof · cited by 113
- Set.union_subsetproof · cited by 71
- Submonoid.subset_closureproof · cited by 46
- Submonoid.closure_leproof · cited by 27
- Submonoid.powers_leproof · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.closure_toSubmonoid_of_finiteproof · cited by 0