Theorems · Theorem · group theory
AddAction.IsPreprimitive.isCoatom_stabilizer_of_isPreprimitive
∀ (G : Type u_3) [inst : AddGroup G] {X : Type u_4} [inst_1 : AddAction G X] [Nontrivial X]
[AddAction.IsPreprimitive G X] (a : X), IsCoatom (AddAction.stabilizer G a)In a preprimitive action, stabilizers are maximal subgroups.
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- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- Nontrivialstatement and proof · cited by 2,416
- AddActionstatement and proof · cited by 820
- IsCoatomstatement · cited by 114
- AddAction.stabilizerstatement · cited by 112
- AddAction.IsPreprimitivestatement and proof · cited by 25
- AddAction.isCoatom_stabilizer_iff_preprimitiveproof · cited by 1
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