Theorems · Theorem · group theory
MulAction.IsBlock.of_orbit
∀ {G : Type u_1} [inst : Group G] {X : Type u_2} [inst_1 : MulAction G X] {H : Subgroup G} {a : X},
MulAction.stabilizer G a ≤ H → MulAction.IsBlock G (MulAction.orbit (↥H) a)The orbit of a under a subgroup containing the stabilizer of a is a block
- Defined in
- Mathlib.GroupTheory.GroupAction.Blocks
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 66 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.
- Setproof · cited by 53,352
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Set.Nonemptyproof · cited by 2,627
- MulActionstatement and proof · cited by 1,294
- SemigroupAction.mul_smulproof · cited by 291
- MulAction.stabilizerstatement and proof · cited by 254
- MulAction.orbitstatement and proof · cited by 114
- MulAction.IsBlockstatement · cited by 73
- Submonoid.smul_defproof · cited by 42
- mul_mem_cancel_rightproof · cited by 11
- mul_mem_cancel_leftproof · cited by 10
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