Theorems · Theorem · group theory
Subgroup.exists_pow_mem_of_relIndex_ne_zero
∀ {G : Type u_1} [inst : Group G] {H K : Subgroup G},
H.relIndex K ≠ 0 → ∀ {a : G}, a ∈ K → ∃ n, 0 < n ∧ n ≤ H.relIndex K ∧ a ^ n ∈ H ⊓ K- 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.
Cites7
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
- Subgroup.indexproof · cited by 150
- Subgroup.subgroupOfproof · cited by 122
- Subgroup.relIndexstatement and proof · cited by 72
- 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.
- isCusp_iff_of_relIndex_ne_zeroproof · cited by 2