Theorems · Theorem · group theory

SpecialLinearGroup.mem_center_iff

∀ {R : Type u_1} {V : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup V] [inst_2 : Module R V] [Module.Free R V]
  [Module.Finite R V] {g : SpecialLinearGroup R V},
  g ∈ Subgroup.center (SpecialLinearGroup R V) ↔ ∃ r, r ^ Module.finrank R V = 1 ∧ ↑↑g = r • LinearMap.id

Defined in

Mathlib.LinearAlgebra.SpecialLinearGroup

Cited by

2 results in Mathlib

Foundations

Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleModule.FreeModule.Finite