Theorems · Theorem · group theory
orbit_subgroup_one_eq_self
∀ {α : Type u_1} [inst : Group α] (s : Subgroup α), MulAction.orbit (↥s) 1 = ↑s- Defined in
- Mathlib.GroupTheory.Coset.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- SetLike.coestatement · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- MulAction.orbitstatement · cited by 114
- Subgroup.one_memproof · cited by 31
- orbit_subgroup_eq_self_of_memproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Nat.card_zpowersproof · cited by 13