Theorems · Theorem · group theory
Subgroup.orderOf_mk
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G} (a : G) (ha : a ∈ H), orderOf ⟨a, ha⟩ = orderOf a- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 39 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- orderOfstatement · cited by 324
- Subgroup.orderOf_coeproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- HasEnoughRootsOfUnity.natCard_rootsOfUnityproof · cited by 5
- Equiv.Perm.alternatingGroup_le_of_isPreprimitive_of_isThreeCycle_memproof · cited by 2
- alternatingGroup.coe_two_sylow_of_card_eq_fourproof · cited by 2
- NumberField.Units.dvd_torsionOrder_of_isPrimitiveRootproof · cited by 1
- Subgroup.orderOf_dvd_natCardproof · cited by 1
- IsPGroup.disjoint_of_coprimeproof · cited by 1
- alternatingGroup.exponent_kleinFour_of_card_eq_fourproof · cited by 1
- Group.card_dvd_prod_orderOfproof · cited by 0