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Theorems · Theorem · group theory

smul_mem_fixedPoints_of_normal

∀ {G : Type u_1} [inst : Group G] {α : Type u_2} [inst_1 : MulAction G α] {H : Subgroup G} [hH : H.Normal] (g : G)
  {a : α}, a ∈ MulAction.fixedPoints (↥H) α → g • a ∈ MulAction.fixedPoints (↥H) α
Defined in
Mathlib.GroupTheory.GroupAction.SubMulAction
Cited by
0 results in Mathlib
Foundations
Depth 23 from the axioms · uses propext
Assumes
GroupMulActionSubgroup.Normal
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Around this declaration

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fixedPointsSubMulOfNormal · cited by 0fixedPointsSubMulOfNormalSet · cited by 53352SetGroup · cited by 6238GroupSubgroup · cited by 3593SubgroupMulAction · cited by 1294MulActionsmul_smul · cited by 360smul_smulSubgroup.Normal · cited by 334Subgroup.NormalMulAction.fixedPoints · cited by 41MulAction.fixedPointsinv_smul_eq_iff · cited by 16inv_smul_eq_iffSubgroup.Normal.conj_mem' · cited by 7Normal.conj_mem'Subgroup.smul_def · cited by 6Subgroup.smul_defsmul_mem_fixedPoints_of_normalCITED BYCITES

Cites10

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Cited by1

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