Theorems · Definition · group theory
DihedralGroup.oddCommuteEquiv
{n : ℕ} → Odd n → { p // Commute p.1 p.2 } ≃ ZMod n ⊕ ZMod n ⊕ ZMod n ⊕ ZMod n × ZMod nIf n is odd, then the Dihedral group of order $2n$ has $n(n+3)$ pairs (represented as $n + n + n + n*n$) of commuting elements.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Equivstatement · cited by 8,337
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- ZModstatement and proof · cited by 1,024
- Commutestatement and proof · cited by 639
- Oddstatement and proof · cited by 364
- DihedralGroupstatement and proof · cited by 41
- ZMod.unitOfCoprimeproof · cited by 20
- ZMod.add_self_eq_zero_iff_eq_zeroproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- DihedralGroup.card_commute_oddproof · cited by 1
- DihedralGroup.oddCommuteEquiv_applystatement and proof · cited by 0
- DihedralGroup.oddCommuteEquiv_symm_applystatement and proof · cited by 0