Theorems · Theorem · group theory
AddAction.stabilizer_orbit_eq
∀ {G : Type u_1} [inst : AddGroup G] {X : Type u_2} [inst_1 : AddAction G X] {a : X} {H : AddSubgroup G},
AddAction.stabilizer G a ≤ H → AddAction.stabilizer G (AddAction.orbit (↥H) a) = HA subgroup containing the stabilizer of a
is the stabilizer of the orbit of a under that subgroup
- Defined in
- Mathlib.GroupTheory.GroupAction.Blocks
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- HVAdd.hVAddproof · cited by 1,820
- AddActionstatement and proof · cited by 820
- VAddproof · cited by 616
- AddAction.stabilizerstatement and proof · cited by 112
- AddSubgroup.toAddSubmonoidproof · cited by 91
- AddAction.orbitstatement and proof · cited by 86
- AddSubgroup.extproof · cited by 75
- AddSemigroupAction.add_vaddproof · cited by 43
- Set.addActionSetstatement · cited by 39
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