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Theorems · Theorem · group theory

AddAction.mem_fixedBy_zmultiples_iff_mem_fixedBy

∀ {α : Type u_1} {G : Type u_2} [inst : AddGroup G] [inst_1 : AddAction G α] {g : G} {a : α},
  (∀ (j : ℤ), a ∈ AddAction.fixedBy α (j • g)) ↔ a ∈ AddAction.fixedBy α g
Defined in
Mathlib.GroupTheory.GroupAction.FixedPoints
Cited by
0 results in Mathlib
Foundations
Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddGroupAddAction
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Set · cited by 53352SetAddGroup · cited by 4410AddGroupAddAction · cited by 820AddActionone_nsmul · cited by 63one_nsmulAddAction.fixedBy · cited by 26AddAction.fixedByofNat_zsmul · cited by 24ofNat_zsmulAddAction.mem_fixedBy · cited by 12AddAction.mem_fixedByAddAction.mem_fixedBy_zsmul · cited by 2AddAction.mem_fixedBy_zsm…AddAction.mem_fixedBy_zmultip…CITED BYCITES

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