Theorems · Theorem · group theory
MulAction.stabilizer_orbit_eq
∀ {G : Type u_1} [inst : Group G] {X : Type u_2} [inst_1 : MulAction G X] {a : X} {H : Subgroup G},
MulAction.stabilizer G a ≤ H → MulAction.stabilizer G (MulAction.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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Cites15
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
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- MulActionstatement and proof · cited by 1,294
- MulAction.stabilizerstatement and proof · cited by 254
- Subgroup.toSubmonoidproof · cited by 114
- MulAction.orbitstatement and proof · cited by 114
- Subgroup.extproof · cited by 108
- Set.mulActionSetstatement · cited by 95
- Submonoid.smul_defproof · cited by 42
- MulAction.mem_stabilizer_iffproof · cited by 20
- mul_mem_cancel_rightproof · cited by 11
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