Theorems · Theorem · group theory
Subgroup.pow_mem_of_index_ne_zero_of_dvd
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G},
H.index ≠ 0 → ∀ (a : G) {n : ℕ}, (∀ (m : ℕ), 0 < m → m ≤ H.index → m ∣ n) → a ^ n ∈ H- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 99 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.
Cites6
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
- pow_mulproof · cited by 210
- Subgroup.indexstatement and proof · cited by 150
- pow_memproof · cited by 46
- Subgroup.exists_pow_mem_of_index_ne_zeroproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.pow_mem_of_relIndex_ne_zero_of_dvdproof · cited by 0