Mathlib Map

Theorems · Definition · group theory

SubAddAction.fixingAddSubgroupInsertEquiv

{M : Type u_1} →
  {α : Type u_2} →
    [inst : AddGroup M] →
      [inst_1 : AddAction M α] →
        (a : α) →
          (s : Set ↥(SubAddAction.ofStabilizer M a)) →
            ↥(fixingAddSubgroup M (insert a (Subtype.val '' s))) ≃+ ↥(fixingAddSubgroup (↥(AddAction.stabilizer M a)) s)

The natural additive group isomorphism between fixing additive subgroups.

Defined in
Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup
Cited by
3 results in Mathlib
Foundations
Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddGroupAddAction
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SubAddAction.ofFixingAddSubgroup_insert_map · cited by 2SubAddAction.ofFixingAddS…SubAddAction.ofFixingAddSubgroup_insert_map_bijective · cited by 2SubAddAction.ofFixingAddS…AddAction.isPreprimitive_fixingAddSubgroup_insert_iff · cited by 1AddAction.isPreprimitive_…SubAddAction.ofFixingAddSubgroup_insert_map_apply · cited by 0SubAddAction.ofFixingAddS…Set · cited by 53352SetSet.image · cited by 5609Set.imageAddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupAddEquiv · cited by 1087AddEquivAddAction · cited by 820AddActionAddAction.stabilizer · cited by 112AddAction.stabilizerSubAddAction · cited by 86SubAddActionfixingAddSubgroup · cited by 50fixingAddSubgroupSubAddAction.ofStabilizer · cited by 29SubAddAction.ofStabilizerSubAddAction.fixingAddSubgrou…CITED BYCITES

Cites10

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Cited by4

Results whose statement or proof uses this declaration.