Theorems · Theorem · group theory
isCyclic_iff_exists_zpowers_eq_top
∀ {α : Type u_1} [inst : Group α], IsCyclic α ↔ ∃ g, Subgroup.zpowers g = ⊤- Cited by
- 4 results in Mathlib
- Foundations
- Depth 71 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Subgroup.zpowersstatement and proof · cited by 204
- IsCyclicstatement and proof · cited by 122
Cited by4
Results whose statement or proof uses this declaration.
- Subgroup.isCyclic_iff_exists_zpowers_eq_topproof · cited by 4
- IsCyclic.card_powMonoidHom_rangeproof · cited by 1
- Subgroup.discrete_iff_cyclicproof · cited by 0
- exists_prime_addEquiv_ZModproof · cited by 0