Theorems · Theorem · number theory
Subgroup.adjoinNegOne_eq_self_iff
∀ {n : Type u_1} [inst : Fintype n] [inst_1 : DecidableEq n] {R : Type u_2} [inst_2 : Ring R] {𝒢 : Subgroup (GL n R)},
𝒢.adjoinNegOne = 𝒢 ↔ -1 ∈ 𝒢- Cited by
- 2 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEqRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Ringstatement and proof · cited by 7,463
- Matrixstatement · cited by 4,303
- Subgroupstatement and proof · cited by 3,593
- one_mulproof · cited by 2,841
- neg_negproof · cited by 960
- neg_mulproof · cited by 654
- mul_negproof · cited by 590
- Matrix.GeneralLinearGroupstatement and proof · cited by 556
- MulMemClass.mul_memproof · cited by 173
- LE.le.antisymm'proof · cited by 104
- Subgroup.adjoinNegOnestatement and proof · cited by 14
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.strictPeriods_eq_periods_of_neg_one_memproof · cited by 1
- Subgroup.relIndex_adjoinNegOne_ne_zeroproof · cited by 1