Theorems · Inductive type · group theory
Subgroup
(G : Type u_3) → [Group G] → Type u_3
A subgroup of a group G is a subset containing 1, closed under multiplication
and closed under multiplicative inverse.
[Wikidata Q466109](https://www.wikidata.org/wiki/Q466109)
- Defined in
- Mathlib.Algebra.Group.Subgroup.Defs
- Cited by
- 3,593 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement · cited by 6,238
Cited by4,338
Results whose statement or proof uses this declaration.
- Subgroup.Normalstatement · cited by 334
- MonoidHom.rangestatement · cited by 314
- Subgroup.mapstatement and proof · cited by 301
- MulAction.stabilizerstatement · cited by 254
- MonoidHom.kerstatement · cited by 212
- Subgroup.zpowersstatement · cited by 204
- Subgroup.closurestatement and proof · cited by 196
- QuotientGroup.mkstatement and proof · cited by 196
- Subgroup.subtypestatement and proof · cited by 185
- MonoidWithZeroHom.valueGroupstatement · cited by 170
- Subgroup.comapstatement and proof · cited by 154
- Subgroup.indexstatement and proof · cited by 150
Showing the 200 most cited of 4,338.