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Theorems · Theorem · group theory

Matrix.SpecialLinearGroup.toPGL_ker

∀ {n : Type u_1} {R : Type u_2} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommRing R],
  Matrix.SpecialLinearGroup.toPGL.ker = Subgroup.center (Matrix.SpecialLinearGroup n R)
Defined in
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Projective
Cited by
1 results in Mathlib
Foundations
Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FintypeDecidableEqCommRing
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Around this declaration

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

Matrix.ProjectiveSpecialLinearGroup.toPGL_injective · cited by 0ProjectiveSpecialLinearGr…CommRing · cited by 17173CommRingFintype · cited by 7736FintypeSubgroup · cited by 3593SubgroupMatrix.SpecialLinearGroup · cited by 348Matrix.SpecialLinearGroupMonoidHom.ker · cited by 212MonoidHom.kerSubgroup.center · cited by 121Subgroup.centerSubgroup.ext · cited by 108Subgroup.extMatrix.ProjGenLinGroup · cited by 23Matrix.ProjGenLinGroupMatrix.SpecialLinearGroup.toPGL · cited by 2SpecialLinearGroup.toPGLSpecialLinearGroup.toPGL_kerCITED BYCITES

Cites9

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Cited by1

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