Theorems · Theorem · group theory
Matrix.GeneralLinearGroup.isParabolic_iff_of_upperTriangular
∀ {K : Type u_2} [inst : Field K] {g : GL (Fin 2) K}, ↑g 1 0 = 0 → (g.IsParabolic ↔ ↑g 0 0 = ↑g 1 1 ∧ ↑g 0 1 ≠ 0)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Matrixstatement · cited by 4,303
- Units.valstatement and proof · cited by 1,966
- Matrix.GeneralLinearGroupstatement and proof · cited by 556
- Matrix.GeneralLinearGroup.IsParabolicstatement · cited by 14
- Matrix.isParabolic_iff_of_upperTriangularproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Subgroup.isCusp_of_mem_strictPeriodsproof · cited by 6
- Subgroup.strictWidthInfty_pos_iffproof · cited by 5
- Matrix.GeneralLinearGroup.isParabolic_iff_of_upperTriangular_of_detproof · cited by 1