Theorems · Definition · group theory
zmodAddCyclicAddEquiv
{G : Type u_2} → [inst : AddGroup G] → IsAddCyclic G → ZMod (Nat.card G) ≃+ GAn arbitrary isomorphism from ZMod n to any cyclic additive group of Nat.card equal to n.
See zmodAddCyclicAddEquiv for a version which doesn't require an explicit generator,
and instead picks one out with the axiom of choice.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddEquivstatement · cited by 1,087
- ZModstatement · cited by 1,024
- Nat.cardstatement · cited by 844
- IsAddCyclicstatement and proof · cited by 55
- zmodAddEquivOfGeneratorproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- zmodCyclicMulEquivproof · cited by 5
- addEquivOfAddCyclicCardEqproof · cited by 0
- exists_prime_addEquiv_ZModproof · cited by 0