Theorems · Theorem · group theory
orderOf_eq_card_of_zpowers_eq_top
∀ {G : Type u_2} [inst : Group G] {g : G}, Subgroup.zpowers g = ⊤ → orderOf g = Nat.card G- Cited by
- 2 results in Mathlib
- Foundations
- Depth 97 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Nat.cardstatement · cited by 844
- Eq.geproof · cited by 375
- orderOfstatement · cited by 324
- Subgroup.zpowersstatement and proof · cited by 204
- Subgroup.mem_topproof · cited by 20
- orderOf_eq_card_of_forall_mem_zpowersproof · cited by 13
Cited by2
Results whose statement or proof uses this declaration.
- IsCyclic.card_powMonoidHom_rangeproof · cited by 1
- exists_prime_addEquiv_ZModproof · cited by 0