Theorems · Theorem · group theory
AddAction.IsBlock.of_orbit
∀ {G : Type u_1} [inst : AddGroup G] {X : Type u_2} [inst_1 : AddAction G X] {H : AddSubgroup G} {a : X},
AddAction.stabilizer G a ≤ H → AddAction.IsBlock G (AddAction.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 64 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites18
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- Setproof · cited by 53,352
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Set.Nonemptyproof · cited by 2,627
- HVAdd.hVAddproof · cited by 1,820
- AddActionstatement and proof · cited by 820
- AddAction.stabilizerstatement and proof · cited by 112
- AddAction.orbitstatement and proof · cited by 86
- AddAction.IsBlockstatement · cited by 65
- AddSemigroupAction.add_vaddproof · cited by 43
- AddAction.mem_stabilizer_iffproof · cited by 27
- neg_vadd_eq_iffproof · cited by 13
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