Theorems · Theorem · group theory
Subgroup.mem_zpowers_iff
∀ {G : Type u_1} [inst : Group G] {g h : G}, h ∈ Subgroup.zpowers g ↔ ∃ k, g ^ k = h- Cited by
- 10 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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 · cited by 3,593
- Subgroup.zpowersstatement · cited by 204
Cited by10
Results whose statement or proof uses this declaration.
- monoidHomOfForallMemZpowers_apply_genproof · cited by 4
- Valuation.exists_pow_Uniformizerproof · cited by 3
- MonoidHom.eq_iff_eq_on_generatorproof · cited by 2
- smul_eq_self_of_mem_zpowersproof · cited by 1
- Subgroup.zpow_mem_zpowersproof · cited by 1
- Subgroup.zpowers_eq_zpowers_iffproof · cited by 1
- Equiv.Perm.OnCycleFactors.kerParam_applyproof · cited by 1
- Subgroup.le_zpowers_iffproof · cited by 0
- orderOf_dvd_of_mem_zpowersproof · cited by 0
- IsOfFinOrder.of_mem_zpowersproof · cited by 0