Theorems · Theorem · group theory
Subgroup.IsSubnormal.smul
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G} {Γ : Type u_2} [inst_1 : Group Γ] [inst_2 : MulDistribMulAction Γ G],
H.IsSubnormal → ∀ (g : Γ), (g • H).IsSubnormalIf g : Γ is an element of a group acting on G and H is subnormal, then g • H is subnormal.
- Defined in
- Mathlib.GroupTheory.IsSubnormal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- MulDistribMulActionstatement and proof · cited by 120
- Subgroup.pointwiseMulActionstatement · cited by 66
- Subgroup.IsSubnormalstatement and proof · cited by 19
- MulAction.surjectiveproof · cited by 5
- Subgroup.IsSubnormal.mapproof · cited by 2
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