Theorems · Theorem · group theory
Equiv.Perm.subgroup_eq_top_of_isPreprimitive_of_isSwap_mem
∀ {α : Type u_1} {G : Subgroup (Equiv.Perm α)} [inst : DecidableEq α] [Finite α],
MulAction.IsPreprimitive (↥G) α → ∀ (g : Equiv.Perm α), g.IsSwap → g ∈ G → G = ⊤A primitive subgroup of Equiv.Perm α that contains a swap
is the full permutation group (Jordan).
- Defined in
- Mathlib.GroupTheory.GroupAction.Jordan
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites52
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Top.topstatement · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Fintypeproof · cited by 7,736
- Set.ofPredproof · cited by 6,101
- Subgroupstatement and proof · cited by 3,593
- Finset.univproof · cited by 3,473
- Finitestatement and proof · cited by 3,029
- Compl.complproof · cited by 2,925
- Finset.cardproof · cited by 2,327
- le_antisymmproof · cited by 2,068
Cited by1
Results whose statement or proof uses this declaration.
- Equiv.Perm.isCoatom_stabilizer_of_ncard_lt_ncard_complproof · cited by 1