Theorems · Theorem · group theory
alternatingGroup.coe_kleinFour_of_card_eq_four
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Fintype α],
Nat.card α = 4 → ↑(alternatingGroup.kleinFour α) = {1} ∪ {g | (↑g).cycleType = {2, 2}}- Cited by
- 3 results in Mathlib
- Foundations
- Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintype
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.
- Setstatement · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Fintypestatement and proof · cited by 7,736
- Set.ofPredstatement and proof · cited by 6,101
- Subgroupstatement and proof · cited by 3,593
- Multisetstatement · cited by 2,627
- Equiv.Permstatement and proof · cited by 1,375
- Nat.cardstatement and proof · cited by 844
- Sylowproof · cited by 103
- alternatingGroupstatement and proof · cited by 96
- Equiv.Perm.cycleTypestatement and proof · cited by 87
- alternatingGroup.kleinFourstatement · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- alternatingGroup.mem_map_kleinFour_ofSubtypeproof · cited by 1
- alternatingGroup.exponent_kleinFour_of_card_eq_fourproof · cited by 1
- alternatingGroup.kleinFour_eq_commutatorproof · cited by 0