Theorems · Definition · group theory
PresentedGroup
{α : Type u_1} → Set (FreeGroup α) → Type u_1Given a set of relations, rels, over a type α, PresentedGroup constructs the group with
generators x : α and relations rels as a quotient of FreeGroup α.
- Defined in
- Mathlib.GroupTheory.PresentedGroup
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- HasQuotient.Quotientproof · cited by 2,301
- FreeGroupstatement and proof · cited by 132
- Subgroup.normalClosureproof · cited by 35
Cited by29
Results whose statement or proof uses this declaration.
- PresentedGroup.ofstatement · cited by 12
- CoxeterMatrix.Groupproof · cited by 11
- PresentedGroup.mkstatement · cited by 10
- CoxeterSystem.simple_mul_simple_selfproof · cited by 9
- PresentedGroup.one_of_memstatement · cited by 3
- PresentedGroup.toCoprodstatement · cited by 3
- PresentedGroup.toGroupstatement · cited by 3
- PresentedGroup.equivPresentedGroupstatement · cited by 2
- CoxeterSystem.subgroup_closure_range_simpleproof · cited by 1
- PresentedGroup.closure_range_ofstatement and proof · cited by 1
- PresentedGroup.extstatement and proof · cited by 1
- PresentedGroup.lift_toCoprod_inl_eq_inl_mkstatement · cited by 1