Theorems · Theorem · group theory
alternatingGroup.kleinFour_card_of_card_eq_four
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Fintype α],
Nat.card α = 4 → Nat.card ↥(alternatingGroup.kleinFour α) = 4- 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Subgroupstatement and proof · cited by 3,593
- 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
- alternatingGroup.kleinFourstatement · cited by 11
- alternatingGroup.two_sylow_eq_kleinFour_of_card_eq_fourproof · cited by 4
- alternatingGroup.card_two_sylow_of_card_eq_fourproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- alternatingGroup.exponent_kleinFour_of_card_eq_fourproof · cited by 1
- alternatingGroup.kleinFour_eq_commutatorproof · cited by 0
- alternatingGroup.kleinFour_isKleinFourproof · cited by 0