Theorems · Theorem · group theory
Subgroup.le_zpowers_iff
∀ {G : Type u_2} [inst : Group G] (g : G) (H : Subgroup G), H ≤ Subgroup.zpowers g ↔ ∃ n, H = Subgroup.zpowers (g ^ n)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 79 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.
Cites12
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
- zpow_natCastproof · cited by 271
- Subgroup.zpowersstatement and proof · cited by 204
- zpow_negproof · cited by 198
- Subgroup.mem_zpowersproof · cited by 12
- Subgroup.zpowers_invproof · cited by 11
- Subgroup.mem_zpowers_iffproof · cited by 10
- Subgroup.isCyclic_iff_exists_zpowers_eq_topproof · cited by 4
- Subgroup.isCyclic_of_leproof · cited by 3
- Subgroup.zpowers_le_of_memproof · cited by 2
- Subgroup.npow_mem_zpowersproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.