Theorems · Theorem · group theory
SpecialLinearGroup.center_eq_bot_of_finrank_le_one
∀ {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], Module.finrank R V ≤ 1 → Subgroup.center (SpecialLinearGroup R V) = ⊥- Defined in
- Mathlib.LinearAlgebra.SpecialLinearGroup
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Bot.botstatement and proof · cited by 4,720
- Subgroupstatement · cited by 3,593
- Nontrivialproof · cited by 2,416
- Module.finrankstatement and proof · cited by 1,770
- Module.Basisproof · cited by 1,477
- Module.Finitestatement and proof · cited by 1,032
- Module.Freestatement and proof · cited by 597
- Matrix.SpecialLinearGroupproof · cited by 348
- Nat.card_eq_fintype_cardproof · cited by 200
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.