Theorems · Theorem · group theory
alternatingGroup.center_eq_bot
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α], 4 ≤ Nat.card α → Subgroup.center ↥(alternatingGroup α) = ⊥- Cited by
- 2 results in Mathlib
- Foundations
- Depth 93 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.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fintypestatement and proof · cited by 7,736
- Bot.botstatement · cited by 4,720
- mul_oneproof · cited by 3,885
- Subgroupstatement · cited by 3,593
- Compl.complproof · cited by 2,925
- Finset.cardproof · cited by 2,327
- Equiv.Permstatement and proof · cited by 1,375
- MulActionproof · cited by 1,294
- neg_negproof · cited by 960
- Nat.cardstatement and proof · cited by 844
- mul_negproof · cited by 590
Cited by2
Results whose statement or proof uses this declaration.
- alternatingGroup.isMulCommutative_iff_card_le_threeproof · cited by 1
- alternatingGroup.kleinFour_eq_commutatorproof · cited by 0