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Theorems · Theorem · group theory

fixedPoints_subgroup_sup

∀ (M : Type u_1) (α : Type u_2) [inst : Group M] [inst_1 : MulAction M α] {P Q : Subgroup M},
  MulAction.fixedPoints (↥(P ⊔ Q)) α = MulAction.fixedPoints (↥P) α ∩ MulAction.fixedPoints (↥Q) α

Fixed points of sup of subgroups is intersection

Defined in
Mathlib.GroupTheory.GroupAction.FixingSubgroup
Cited by
0 results in Mathlib
Foundations
Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
GroupMulAction
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Set · cited by 53352SetGroup · cited by 6238GroupSubgroup · cited by 3593SubgroupMulAction · cited by 1294MulActionMulAction.fixedPoints · cited by 41MulAction.fixedPointsGaloisConnection.u_inf · cited by 37GaloisConnection.u_inffixingSubgroup_fixedPoints_gc · cited by 7fixingSubgroup_fixedPoint…fixedPoints_subgroup_supCITED BYCITES

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