Theorems · Definition · number theory
Subgroup.adjoinNegOne
{n : Type u_1} →
[inst : Fintype n] →
[inst_1 : DecidableEq n] → {R : Type u_2} → [inst_2 : Ring R] → Subgroup (GL n R) → Subgroup (GL n R)Given a subgroup 𝒢 of GL n R, this is the subgroup generated by 𝒢 and -1.
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 84 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.
Cites6
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
- Set.ofPredproof · cited by 6,101
- Matrixstatement · cited by 4,303
- Subgroupstatement and proof · cited by 3,593
- Matrix.GeneralLinearGroupstatement and proof · cited by 556
Cited by16
Results whose statement or proof uses this declaration.
- Subgroup.periodsproof · cited by 10
- Subgroup.widthInftyproof · cited by 7
- Subgroup.le_adjoinNegOnestatement · cited by 5
- Subgroup.adjoinNegOne_eq_self_iffstatement and proof · cited by 2
- Subgroup.negOne_mem_adjoinNegOnestatement · cited by 2
- Subgroup.widthInfty_mem_periodsproof · cited by 2
- Subgroup.relIndex_adjoinNegOne_ne_zerostatement · cited by 1
- Subgroup.commensurable_adjoinNegOne_selfstatement · cited by 1
- Subgroup.periods_eq_zmultiples_widthInftyproof · cited by 1
- Subgroup.relindex_adjoinNegOne_eq_twostatement · cited by 1
- Subgroup.widthInfty_nonnegproof · cited by 0
- Subgroup.widthInfty_posproof · cited by 0