Theorems · Theorem · group theory
alternatingGroup.isMulCommutative_iff_card_le_three
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α], IsMulCommutative ↥(alternatingGroup α) ↔ Nat.card α ≤ 3- Cited by
- 1 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Bot.botproof · cited by 4,720
- Subgroupstatement · cited by 3,593
- LT.lt.leproof · cited by 2,189
- Equiv.Permstatement and proof · cited by 1,375
- Nat.cardstatement and proof · cited by 844
- not_ltproof · cited by 306
- alternatingGroupstatement and proof · cited by 96
- IsMulCommutativestatement and proof · cited by 95
- not_nontrivial_iff_subsingletonproof · cited by 23
- Subgroup.center_eq_top_iffproof · cited by 4
- alternatingGroup.center_eq_botproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- alternatingGroup.isCyclic_iff_card_le_threeproof · cited by 0