Theorems · Definition · group theory
Subgroup.closure
{G : Type u_1} → [inst : Group G] → Set G → Subgroup GThe Subgroup generated by a set.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 196 results in Mathlib
- Foundations
- Depth 66 from the axioms, rests on 747 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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.
- Setstatement and proof · cited by 53,352
- SetLike.coeproof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Set.ofPredproof · cited by 6,101
- Subgroupstatement and proof · cited by 3,593
- InfSet.sInfproof · cited by 935
Cited by214
Results whose statement or proof uses this declaration.
- MonoidWithZeroHom.valueGroupproof · cited by 170
- Subgroup.subset_closurestatement · cited by 53
- Subgroup.normalClosureproof · cited by 35
- Subgroup.closure_lestatement · cited by 31
- Subgroup.FGproof · cited by 18
- MonoidHom.map_closurestatement · cited by 16
- Subgroup.closure_inductionstatement and proof · cited by 14
- RootPairing.weylGroupproof · cited by 14
- alternatingGroup.kleinFourproof · cited by 11
- lipschitzGroupproof · cited by 10
- Subgroup.normalClosure_le_normalproof · cited by 10
- Subgroup.closure_eqstatement · cited by 9
Showing the 200 most cited of 214.