Theorems · Theorem · number theory
Subgroup.relindex_adjoinNegOne_eq_two
∀ {n : Type u_1} [inst : Fintype n] [inst_1 : DecidableEq n] {R : Type u_2} [inst_2 : Ring R] {𝒢 : Subgroup (GL n R)},
-1 ∉ 𝒢 → 𝒢.relIndex 𝒢.adjoinNegOne = 2- Cited by
- 1 results in Mathlib
- Foundations
- Depth 97 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.
Cites11
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
- mul_oneproof · cited by 3,885
- Subgroupstatement and proof · cited by 3,593
- mul_negproof · cited by 590
- Matrix.GeneralLinearGroupstatement and proof · cited by 556
- Subgroup.relIndexstatement · cited by 72
- Subgroup.adjoinNegOnestatement · cited by 14
- Subgroup.negOne_mem_adjoinNegOneproof · cited by 2
- Subgroup.relIndex_eq_two_iff_exists_notMem_andproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.relIndex_adjoinNegOne_ne_zeroproof · cited by 1