Theorems · Theorem · group theory
Fintype.card_zpowers
∀ {G : Type u_1} [inst : Group G] [inst_1 : Fintype G] {x : G}, Fintype.card ↥(Subgroup.zpowers x) = orderOf xSee also Nat.card_zpowers.
- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Fintype.cardstatement · cited by 1,386
- orderOfstatement and proof · cited by 324
- Fintype.card_finproof · cited by 270
- Subgroup.zpowersstatement · cited by 204
- Fintype.card_eqproof · cited by 19
- isOfFinOrder_of_finiteproof · cited by 14
- finEquivZPowersproof · cited by 6
Cited by5
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsCycle.orderOfproof · cited by 14
- orderOf_dvd_cardproof · cited by 9
- IsCyclic.card_pow_eq_one_leproof · cited by 2
- Equiv.Perm.OnCycleFactors.kerParam_range_cardproof · cited by 1
- card_zpowers_leproof · cited by 0