Theorems · Theorem · number theory
Subgroup.IsArithmetic.conj
∀ (𝒢 : Subgroup (GL (Fin 2) ℝ)) [𝒢.IsArithmetic] (g : GL (Fin 2) ℚ), (ConjAct.toConjAct ((Matrix.GeneralLinearGroup.map (Rat.castHom ℝ)) g) • 𝒢).IsArithmetic
Conjugation by GL(2, ℚ) preserves arithmetic subgroups.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Subgroup.IsArithmetic
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Matrixstatement · cited by 4,303
- MonoidHomstatement · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- MulEquivstatement · cited by 1,142
- Matrix.GeneralLinearGroupstatement and proof · cited by 556
- ConjActstatement · cited by 79
- Subgroup.pointwiseMulActionstatement · cited by 66
- ConjAct.toConjActstatement and proof · cited by 56
- Subgroup.IsArithmeticstatement and proof · cited by 41
- Rat.castHomstatement and proof · cited by 33
Cited by1
Results whose statement or proof uses this declaration.
- CuspFormClass.petersson_bounded_leftproof · cited by 2