Theorems · Theorem · group theory
QuotientGroup.out_conj_pow_minimalPeriod_mem
∀ {G : Type u} [inst : Group G] (H : Subgroup G) (g : G) (q : G ⧸ H),
(Quotient.out q)⁻¹ * g ^ Function.minimalPeriod (fun x => g • x) q * Quotient.out q ∈ H- Defined in
- Mathlib.GroupTheory.GroupAction.Quotient
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 73 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.
Cites14
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
- HasQuotient.Quotientstatement and proof · cited by 2,301
- mul_assocproof · cited by 1,667
- smul_eq_mulproof · cited by 357
- QuotientGroup.mkproof · cited by 196
- Quotient.outstatement and proof · cited by 141
- Function.minimalPeriodstatement and proof · cited by 100
- dvd_reflproof · cited by 97
- QuotientGroup.leftRelstatement · cited by 61
- QuotientGroup.eqproof · cited by 20
- QuotientGroup.out_eq'proof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- MonoidHom.transfer_eq_powproof · cited by 2
- MonoidHom.transfer_eq_pow_auxproof · cited by 2
- MonoidHom.transfer_eq_prod_quotient_orbitRel_zpowers_quotstatement and proof · cited by 2
- Subgroup.transferFocal_eq_powproof · cited by 2