Theorems · Definition · group theory
AddEquiv.toMultiplicative
{G : Type u_2} →
{H : Type u_3} → [inst : AddZeroClass G] → [inst_1 : AddZeroClass H] → G ≃+ H ≃ (Multiplicative G ≃* Multiplicative H)Reinterpret G ≃+ H as Multiplicative G ≃* Multiplicative H.
- Defined in
- Mathlib.Algebra.Group.Equiv.TypeTags
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses Quot.sound
- Assumes
- AddZeroClassAddZeroClass
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.
- DFunLike.coeproof · cited by 62,936
- Equivstatement · cited by 8,337
- Equiv.symmproof · cited by 3,681
- AddZeroClassstatement and proof · cited by 1,237
- MulEquivstatement and proof · cited by 1,142
- AddEquivstatement and proof · cited by 1,087
- Multiplicativestatement and proof · cited by 875
- AddEquiv.symmproof · cited by 530
- MulEquiv.symmproof · cited by 482
- MulEquiv.toMonoidHomproof · cited by 126
- AddEquiv.toAddMonoidHomproof · cited by 101
- AddMonoidHom.toMultiplicativeproof · cited by 21
Cited by16
Results whose statement or proof uses this declaration.
- IsCyclic.mulAutMulEquivproof · cited by 6
- MulAutMultiplicativeproof · cited by 6
- zmodCyclicMulEquivproof · cited by 5
- zmodMulEquivOfGeneratorproof · cited by 4
- AddEquiv.toAdditive_toMultiplicativeproof · cited by 2
- IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroModproof · cited by 2
- MulAction.zpowersQuotientStabilizerEquivproof · cited by 1
- Int.subgroup_index_ne_zero_iffproof · cited by 0
- IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_mod_eqproof · cited by 0
- AddEquiv.toMultiplicative_apply_applystatement and proof · cited by 0
- AddEquiv.toMultiplicative_apply_symm_applystatement and proof · cited by 0
- AddEquiv.toMultiplicative_symm_apply_applystatement and proof · cited by 0