Theorems · Definition · group theory
zmodCyclicMulEquiv
{G : Type u_2} → [inst : Group G] → IsCyclic G → Multiplicative (ZMod (Nat.card G)) ≃* GAn arbitrary isomorphism from Multiplicative (ZMod n) to any cyclic group
of Nat.card equal to n.
See zmodMulEquivOfGenerator for a version which takes an explicit generator.
- Cited by
- 5 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Groupstatement and proof · cited by 6,238
- MulEquivstatement · cited by 1,142
- ZModstatement · cited by 1,024
- Multiplicativestatement · cited by 875
- Nat.cardstatement · cited by 844
- IsCyclicstatement and proof · cited by 122
- AddEquiv.toMultiplicativeproof · cited by 8
- zmodAddCyclicAddEquivproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- IsCyclic.mulAutMulEquivproof · cited by 6
- mulEquivOfCyclicCardEqproof · cited by 1
- IsCyclic.mulAutMulEquiv_symm_apply_symm_applystatement · cited by 0
- IsCyclic.val_inv_mulAutMulEquiv_applystatement · cited by 0
- IsCyclic.val_mulAutMulEquiv_applystatement · cited by 0
- zmodCyclicMulEquiv.congr_simpstatement and proof · cited by 0
- IsCyclic.mulAutMulEquiv_symm_apply_applystatement · cited by 0