Theorems · Theorem · number theory
Subgroup.hasDetOne_adjoinNegOne_iff
∀ {n : Type u_1} [inst : Fintype n] [inst_1 : DecidableEq n] {R : Type u_3} [inst_2 : CommRing R]
{𝒢 : Subgroup (GL n R)}, Even (Fintype.card n) → (𝒢.adjoinNegOne.HasDetOne ↔ 𝒢.HasDetOne)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEqCommRing
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Matrixstatement · cited by 4,303
- Subgroupstatement and proof · cited by 3,593
- one_mulproof · cited by 2,841
- Units.valproof · cited by 1,966
- Fintype.cardstatement and proof · cited by 1,386
- Matrix.detproof · cited by 665
- Matrix.GeneralLinearGroupstatement and proof · cited by 556
- one_powproof · cited by 521
- Evenstatement and proof · cited by 444
- Even.neg_powproof · cited by 99
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