Mathlib Map

Theorems · Definition · group theory

SubAddAction.ofFixingAddSubgroup

(M : Type u_1) →
  {α : Type u_2} →
    [inst : AddGroup M] → [inst_1 : AddAction M α] → (s : Set α) → SubAddAction (↥(fixingAddSubgroup M s)) α

The SubAddAction of fixingAddSubgroup M s on the complement of s.

Defined in
Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup
Cited by
32 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddGroupAddAction

Around this declaration

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

AddAction.IsMultiplyPreprimitive.isPreprimitive_ofFixingAddSubgroup · cited by 6IsMultiplyPreprimitive.is…AddAction.isMultiplyPreprimitive_iff · cited by 5AddAction.isMultiplyPrepr…SubAddAction.ofFixingAddSubgroup.append · cited by 3ofFixingAddSubgroup.appendSubAddAction.ofFixingAddSubgroup.isMultiplyPretransitive · cited by 3ofFixingAddSubgroup.isMul…SubAddAction.addConjMap_ofFixingAddSubgroup · cited by 2SubAddAction.addConjMap_o…SubAddAction.map_ofFixingAddSubgroupUnion · cited by 2SubAddAction.map_ofFixing…SubAddAction.mem_ofFixingAddSubgroup_iff · cited by 2SubAddAction.mem_ofFixing…SubAddAction.ofFixingAddSubgroup_equivariantMap · cited by 2SubAddAction.ofFixingAddS…SubAddAction.ofFixingAddSubgroup_insert_map · cited by 2SubAddAction.ofFixingAddS…SubAddAction.ofFixingAddSubgroup_insert_map_bijective · cited by 2SubAddAction.ofFixingAddS…SubAddAction.ofFixingAddSubgroup_of_eq · cited by 2SubAddAction.ofFixingAddS…SubAddAction.addConjMap_ofFixingAddSubgroup_bijective · cited by 1SubAddAction.addConjMap_o…SubAddAction.disjoint_val_image · cited by 1SubAddAction.disjoint_val…AddAction.isMultiplyPreprimitive_ofStabilizer · cited by 1AddAction.isMultiplyPrepr…AddAction.isPreprimitive_fixingAddSubgroup_insert_iff · cited by 1AddAction.isPreprimitive_…Set · cited by 53352SetAddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupCompl.compl · cited by 2925Compl.complAddAction · cited by 820AddActionSubAddAction · cited by 86SubAddActionfixingAddSubgroup · cited by 50fixingAddSubgroupSubAddAction.ofFixingAddSubgr…CITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by43

Results whose statement or proof uses this declaration.