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Theorems · Theorem · group theory

Subgroup.Characteristic.fixed

∀ {G : Type u_1} [inst : Group G] {H : Subgroup G},
  H.Characteristic → ∀ (ϕ : G ≃* G), Subgroup.comap ϕ.toMonoidHom H = H

H is fixed by all automorphisms

Defined in
Mathlib.Algebra.Group.Subgroup.Basic
Cited by
1 results in Mathlib
Foundations
Depth 22 from the axioms · uses propext, Quot.sound
Assumes
Group
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Around this declaration

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

Subgroup.characteristic_iff_comap_eq · cited by 4Subgroup.characteristic_i…Group · cited by 6238GroupSubgroup · cited by 3593SubgroupMulEquiv · cited by 1142MulEquivSubgroup.comap · cited by 154Subgroup.comapMulEquiv.toMonoidHom · cited by 126MulEquiv.toMonoidHomSubgroup.Characteristic · cited by 20Subgroup.CharacteristicCharacteristic.fixedCITED BYCITES

Cites6

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Cited by1

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