Theorems · Theorem · group theory
alternatingGroup.characteristic_kleinFour
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Fintype α],
Nat.card α = 4 → (alternatingGroup.kleinFour α).Characteristic- Cited by
- 1 results in Mathlib
- Foundations
- Depth 127 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.
Cites10
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
- Subgroup.Characteristicstatement and proof · cited by 20
- alternatingGroup.kleinFourstatement · cited by 11
- alternatingGroup.two_sylow_eq_kleinFour_of_card_eq_fourproof · cited by 4
- alternatingGroup.subsingleton_two_sylowproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- alternatingGroup.normal_kleinFourproof · cited by 1