Theorems · Theorem · group theory
Matrix.GeneralLinearGroup.IsParabolic.pow
∀ {K : Type u_2} [inst : Field K] {g : GL (Fin 2) K},
g.IsParabolic → ∀ [CharZero K] {n : ℕ}, n ≠ 0 → (g ^ n).IsParabolicA non-zero power of a parabolic element is parabolic.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites33
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Matrixstatement and proof · cited by 4,303
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- zero_addproof · cited by 2,366
- Units.valproof · cited by 1,966
- map_zeroproof · cited by 1,614
- one_smulproof · cited by 1,374
- pow_zeroproof · cited by 1,094
Cited by2
Results whose statement or proof uses this declaration.
- isCusp_iff_of_relIndex_ne_zeroproof · cited by 2
- Matrix.GeneralLinearGroup.IsParabolic.parabolicFixedPoint_powproof · cited by 1