Theorems · Theorem · group theory
Equiv.Perm.card_le_of_centralizer_le_alternating
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] {g : Equiv.Perm α},
Subgroup.centralizer {g} ≤ alternatingGroup α → Fintype.card α ≤ g.cycleType.sum + 1- Cited by
- 1 results in Mathlib
- Foundations
- Depth 107 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
- Setstatement · cited by 53,352
- Fintypestatement and proof · cited by 7,736
- Set.Elemproof · cited by 7,166
- mul_oneproof · cited by 3,885
- Subgroupstatement · cited by 3,593
- Finset.prodproof · cited by 2,356
- Fintype.cardstatement and proof · cited by 1,386
- Equiv.Permstatement and proof · cited by 1,375
- Multiset.sumstatement and proof · cited by 388
- Set.mem_range_selfproof · cited by 328
- Equiv.Perm.supportproof · cited by 230
Cited by1
Results whose statement or proof uses this declaration.
- Equiv.Perm.centralizer_le_alternating_iffproof · cited by 0